engineering problem solving method

Oct 13, 2019

10 Steps to Problem Solving for Engineers

Updated: Dec 6, 2020

With the official launch of the engineering book 10+1 Steps to Problem Solving: An Engineer's Guide it may be interesting to know that formalization of the concept began in episode 2 of the Engineering IRL Podcast back in July 2018.

As noted in the book remnants of the steps had existed throughout my career and in this episode I actually recorded the episode off the top of my head.

My goal was to help engineers build a practical approach to problem solving.

Have a listen.

Who can advise on the best approach to problem solving other than the professional problem solvers - Yes. I'm talking about being an Engineer.

There are 2 main trains of thought with Engineering work for non-engineers and that's trying to change the world with leading edge tech and innovations, or plain old boring math nerd type things.

Whilst, somewhat the case what this means is most content I read around Tech and Engineering are either super technical and (excruciatingly) detailed. OR really riff raff at the high level reveling at the possibilities of changing the world as we know it. And so what we end up with is a base (engineer only details) and the topping (media innovation coverage) but what about the meat? The contents?

There's a lot of beauty and interesting things there too. And what's the centrepiece? The common ground between all engineers? Problem solving.

The number one thing an Engineer does is problem solving. Now you may say, "hey, that's the same as my profession" - well this would be true for virtually every single profession on earth. This is not saying there isn't problem solving required in other professions. Some problems require very basic problem solving techniques such is used in every day life, but sometimes problems get more complicated, maybe they involve other parties, maybe its a specific quirk of the system in a specific scenario. One thing you learn in engineering is that not all problems are equal. These are

The stages of problem solving like a pro:

Is the problem identified (no, really, are you actually asking the right question?)

Have you applied related troubleshooting step to above problem?

Have you applied basic troubleshooting steps (i.e. check if its plugged in, turned it on and off again, checked your basics)

Tried step 2 again? (Desperation seeps in, but check your bases)

Asked a colleague or someone else that may have dealt with your problem? (50/50 at this point)

Asked DR. Google (This is still ok)

Deployed RTFM protocol (Read the F***ing Manual - Engineers are notorious for not doing this)

Repeated tests, changing slight things, checking relation to time, or number of people, or location or environment (we are getting DEEP now)

Go to the bottom level, in networking this is packet sniffers to inspect packets, in systems this is taking systems apart and testing in isolation, in software this is checking if 1 equals 1, you are trying to prove basic human facts that everyone knows. If 1 is not equal to 1, you're in deep trouble.At this point you are at rebuild from scratch, re install, start again as your answer (extremely expensive, very rare)

And there you have it! Those are your levels of problem solving. As you go through each step, the more expensive the problem is. -- BUT WAIT. I picked something up along the way and this is where I typically thrive. Somewhere between problem solving step 8 and 10.

The secret step

My recommendation at this point is to try tests that are seemingly unrelated to anything to do with the problem at all.Pull a random cable, test with a random system off/on, try it at a specific time of the day, try it specifically after restarting or replugging something in. Now, not completely random but within some sort of scope. These test are the ones that when someone is having a problem when you suggest they say "that shouldn't fix the problem, that shouldn't be related" and they are absolutely correct.But here's the thing -- at this stage they have already tried everything that SHOULD fix the problem. Now it's time for the hail mary's, the long shots, the clutching at straws. This method works wonders for many reasons. 1. You really are trying to try "anything" at this point.

2. Most of the time we may think we have problem solving step number 1 covered, but we really don't.

3. Triggering correlations.

This is important.

Triggering correlations

In a later post I will cover correlation vs causation, but for now understand that sometimes all you want to do is throw in new inputs to the system or problem you are solving in order to get clues or re identify problems or give new ways to approach earlier problem solving steps. There you have it. Problem solve like a ninja. Approach that extremely experienced and smart person what their problem and as they describe all the things they've tried, throw in a random thing they haven't tried. And when they say, well that shouldn't fix it, you ask them, well if you've exhausted everything that should have worked, this is the time to try things that shouldn't. Either they will think of more tests they haven't considered so as to avoid doing your preposterous idea OR they try it and get a new clue to their problem. Heck, at worst they confirm that they do know SOMETHING about the system.

Go out and problem solve ! As always, thanks for reading and good luck with all of your side hustles.

If you prefer to listen to learn we got you covered with the Engineering IRL show!

For Youtube please go to:

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Technical Tactics
10+1 Steps to Problem Solving

Engineering Problem Solving ¶

Some problems are so complex that you have to be highly intelligent and well-informed just to be undecided about them. —Laurence J. Peter

Steps in solving ‘real world’ engineering problems ¶

The following are the steps as enumerated in your textbook:

Collaboratively define the problem

List possible solutions

Evaluate and rank the possible solutions

Develop a detailed plan for the most attractive solution(s)

Re-evaluate the plan to check desirability

Implement the plan

Check the results

A critical part of the analysis process is the ‘last’ step: checking and verifying the results.

Depending on the circumstances, errors in an analysis, procedure, or implementation can have significant, adverse consequences (NASA Mars orbiter crash, Bhopal chemical leak tragedy, Hubble telescope vision issue, Y2K fiasco, BP oil rig blowout, …).

In a practical sense, these checks must be part of a comprehensive risk management strategy.

My experience with problem solving in industry was pretty close to this, though encumbered by numerous business practices (e.g., ‘go/no-go’ tollgates, complex approval processes and procedures).

In addition, solving problems in the ‘real world’ requires a multidisciplinary effort, involving people with various expertise: engineering, manufacturing, supply chain, legal, marketing, product service and warranty, …

Exercise: Problem solving

Step 3 above refers to ranking of alternatives.

Think of an existing product of interest.

What do you think was ranked highest when the product was developed?

Consider what would have happened if a different ranking was used. What would have changed about the product?

Brainstorm ideas with the students around you.

Defining problems collaboratively ¶

Especially in light of global engineering , we need to consider different perspectives as we define our problem. Let’s break the procedure down into steps:

Identify each perspective that is involved in the decision you face. Remember that problems often mean different things in different perspectives. Relevant differences might include national expectations, organizational positions, disciplines, career trajectories, etc. Consider using the mnemonic device “Location, Knowledge, and Desire.”

Location : Who is defining the problem? Where are they located or how are they positioned? How do they get in their positions? Do you know anything about the history of their positions, and what led to the particular configuration of positions you have today on the job? Where are the key boundaries among different types of groups, and where are the alliances?

Knowledge : What forms of knowledge do the representatives of each perspective have? How do they understand the problem at hand? What are their assumptions? From what sources did they gain their knowledge? How did their knowledge evolve?

Desire : What do the proponents of each perspective want? What are their objectives? How do these desires develop? Where are they trying to go? Learn what you can about the history of the issue at hand. Who might have gained or lost ground in previous encounters? How does each perspective view itself at present in relation to those it envisions as relevant to its future?

As formal problem definitions emerge, ask “Whose definition is this?” Remember that “defining the problem clearly” may very well assert one perspective at the expense of others. Once we think about problem solving in relation to people, we can begin to see that the very act of drawing a boundary around a problem has non-technical, or political dimensions, depending on who controls the definition, because someone gains a little power and someone loses a little power.

Map what alternative problem definitions mean to different participants. More than likely you will best understand problem definitions that fit your perspective. But ask “Does it fit other perspectives as well?” Look at those who hold Perspective A. Does your definition fit their location, their knowledge, and their desires? Now turn to those who hold Perspective B. Does your definition fit their location, knowledge, and desires? Completing this step is difficult because it requires stepping outside of one’s own perspective and attempting to understand the problem in terms of different perspectives.

To the extent you encounter disagreement or conclude that the achievement of it is insufficient, begin asking yourself the following: How might I adapt my problem definition to take account of other perspectives out there? Is there some way of accommodating myself to other perspectives rather than just demanding that the others simply recognize the inherent value and rationality of mine? Is there room for compromise among contrasting perspectives?

How ‘good’ a solution do you need ¶

There is also an important aspect of real-world problem solving that is rarely articulated and that is the idea that the ‘quality’ of the analysis and the resources expended should be dependent on the context.

This is difficult to assess without some experience in the particular environment.

How ‘Good’ a Solution Do You Need?

Some rough examples:

10 second answer (answering a question at a meeting in front of your manager or vice president)

10 minute answer (answering a quick question from a colleague)

10 hour answer (answering a request from an important customer)

10 day answer (assembling information as part of a trouble-shooting team)

10 month answer (putting together a comprehensive portfolio of information as part of the design for a new $200,000,000 chemical plant)

Steps in solving well-defined engineering process problems, including textbook problems ¶

Essential steps:

Carefully read the problem statement (perhaps repeatedly) until you understand exactly the scenario and what is being asked.

Translate elements of the word problem to symbols. Also, look for key words that may convey additional information, e.g., ‘steady state’, ‘constant density’, ‘isothermal’. Make note of this additional information on your work page.

Draw a diagram. This can generally be a simple block diagram showing all the input, output, and connecting streams.

Write all known quantities (flow rates, densities, etc.) from step 2 in the appropriate locations on, or near, the diagram. If symbols are used to designate known quantities, include those symbols.

Identify and assign symbols to all unknown quantities and write them in the appropriate locations on, or near, the diagram.

Construct the relevant equation(s). These could be material balances, energy balances, rate equations, etc.

Write down all equations in their general forms. Don’t simplify anything yet.

Discard terms that are equal to zero (or are assumed negligible) for your specific problem and write the simplified equations.

Replace remaining terms with more convenient forms (because of the given information or selected symbols).

Construct equations to express other known relationships between variables, e.g., relationships between stoichiometric coefficients, the sum of species mass fractions must be one.

Whenever possible, solve the equations for the unknown(s) algebraically .

Convert the units of your variables as needed to have a consistent set across your equations.

Substitute these values into the equation(s) from step 7 to get numerical results.

Check your answer.

Does it make sense?

Are the units of the answer correct?

Is the answer consistent with other information you have?

Exercise: Checking results

How do you know your answer is right and that your analysis is correct?

This may be relatively easy for a homework problem, but what about your analysis for an ill-defined ‘real-world’ problem?

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3 What is Problem Solving?

Chapter table of contents, what is problem solving.

What Does Problem Solving Look Like?

Developing Problem Solving Processes

Summary of strategies, problem solving: an important job skill.

The ability to solve problems is a basic life skill and is essential to our day-to-day lives, at home, at school, and at work. We solve problems every day without really thinking about how we solve them. For example: it’s raining and you need to go to the store. What do you do? There are lots of possible solutions. Take your umbrella and walk. If you don’t want to get wet, you can drive, or take the bus. You might decide to call a friend for a ride, or you might decide to go to the store another day. There is no right way to solve this problem and different people will solve it differently.

Problem solving is the process of identifying a problem, developing possible solution paths, and taking the appropriate course of action.

Why is problem solving important? Good problem solving skills empower you not only in your personal life but are critical in your professional life. In the current fast-changing global economy, employers often identify everyday problem solving as crucial to the success of their organizations. For employees, problem solving can be used to develop practical and creative solutions, and to show independence and initiative to employers.

what does problem solving look like?

The ability to solve problems is a skill at which you can improve. So how exactly do you practice problem solving? Learning about different problem solving strategies and when to use them will give you a good start. Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic.

Algorithmic strategies are traditional step-by-step guides to solving problems. They are great for solving math problems (in algebra: multiply and divide, then add or subtract) or for helping us remember the correct order of things (a mnemonic such as “Spring Forward, Fall Back” to remember which way the clock changes for daylight saving time, or “Righty Tighty, Lefty Loosey” to remember what direction to turn bolts and screws). Algorithms are best when there is a single path to the correct solution.

But what do you do when there is no single solution for your problem? Heuristic methods are general guides used to identify possible solutions. A popular one that is easy to remember is IDEAL [Bransford & Stein [1] ] :

IDEAL is just one problem solving strategy. Building a toolbox of problem solving strategies will improve your problem solving skills. With practice, you will be able to recognize and use multiple strategies to solve complex problems.

What is the best way to get a peanut out of a tube that cannot be moved? Watch a chimpanzee solve this problem in the video below [Geert Stienissen [2] ].

Problem solving is a process that uses steps to solve problems. But what does that really mean? Let's break it down and start building our toolbox of problem solving strategies.

What is the first step of solving any problem? The first step is to recognize that there is a problem and identify the right cause of the problem. This may sound obvious, but similar problems can arise from different events, and the real issue may not always be apparent. To really solve the problem, it's important to find out what started it all. This is called identifying the root cause .

Example: You and your classmates have been working long hours on a project in the school's workshop. The next afternoon, you try to use your student ID card to access the workshop, but discover that your magnetic strip has been demagnetized. Since the card was a couple of years old, you chalk it up to wear and tear and get a new ID card. Later that same week you learn that several of your classmates had the same problem! After a little investigation, you discover that a strong magnet was stored underneath a workbench in the workshop. The magnet was the root cause of the demagnetized student ID cards.

The best way to identify the root cause of the problem is to ask questions and gather information. If you have a vague problem, investigating facts is more productive than guessing a solution. Ask yourself questions about the problem. What do you know about the problem? What do you not know? When was the last time it worked correctly? What has changed since then? Can you diagram the process into separate steps? Where in the process is the problem occurring? Be curious, ask questions, gather facts, and make logical deductions rather than assumptions.

When issues and problems arise, it is important that they are addressed in an efficient and timely manner. Communication is an important tool because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost, and save money. Although, each path in this exercise ended with a description of a problem solving tool for your toolbox, the first step is always to identify the problem and define the context in which it happened.

There are several strategies that can be used to identify the root cause of a problem. Root cause analysis (RCA) is a method of problem solving that helps people answer the question of why the problem occurred. RCA uses a specific set of steps, with associated tools like the “5 Why Analysis" or the “Cause and Effect Diagram,” to identify the origin of the problem, so that you can:

Once the underlying cause is identified and the scope of the issue defined, the next step is to explore possible strategies to fix the problem.

If you are not sure how to fix the problem, it is okay to ask for help. Problem solving is a process and a skill that is learned with practice. It is important to remember that everyone makes mistakes and that no one knows everything. Life is about learning. It is okay to ask for help when you don’t have the answer. When you collaborate to solve problems you improve workplace communication and accelerates finding solutions as similar problems arise.

One tool that can be useful for generating possible solutions is brainstorming . Brainstorming is a technique designed to generate a large number of ideas for the solution to a problem. The goal is to come up with as many ideas as you can, in a fixed amount of time. Although brainstorming is best done in a group, it can be done individually.

Depending on your path through the exercise, you may have discovered that a couple of your coworkers had experienced similar problems. This should have been an indicator that there was a larger problem that needed to be addressed.

In any workplace, communication of problems and issues (especially those that involve safety) is always important. This is especially crucial in manufacturing where people are constantly working with heavy, costly, and sometimes dangerous equipment. When issues and problems arise, it is important that they be addressed in an efficient and timely manner. Because it can prevent problems from recurring, avoid injury to personnel, reduce rework and scrap, and ultimately, reduce cost and save money; effective communication is an important tool..

One strategy for improving communication is the huddle . Just like football players on the field, a huddle is a short meeting with everyone standing in a circle. It's always important that team members are aware of how their work impacts one another. A daily team huddle is a great way to ensure that as well as making team members aware of changes to the schedule or any problems or safety issues that have been identified. When done right, huddles create collaboration, communication, and accountability to results. Impromptu huddles can be used to gather information on a specific issue and get each team member's input.

"Never try to solve all the problems at once — make them line up for you one-by-one.” — Richard Sloma

Problem solving improves efficiency and communication on the shop floor. It increases a company's efficiency and profitability, so it's one of the top skills employers look for when hiring new employees. Employers consider professional skills, such as problem solving, as critical to their business’s success.

The 2011 survey, "Boiling Point? The skills gap in U.S. manufacturing [3] ," polled over a thousand manufacturing executives who reported that the number one skill deficiency among their current employees is problem solving, which makes it difficult for their companies to adapt to the changing needs of the industry.

Bransford, J. & Stein, B.S. (). The Ideal Problem Solver: A Guide For Improving Thinking, Learning, And Creativity . New York, NY: W.H. Freeman. ↵
National Geographic. [Geert Stienissen]. (2010, August 19). Insight learning: Chimpanzee Problem Solving [Video file]. Retrieved from http://www.youtube.com/watch?v=fPz6uvIbWZE ↵
Report: Boiling Point: The Skills Gap in U.S. Manufacturing Deloitte / The Manufacturing Institute, October 2011. Retrieved from http://www.themanufacturinginstitute.org/Hidden/2011-Skills-Gap-Report/2011-Skills-Gap-Report.aspx ↵

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1.4: Problem Solving

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Daniel W. Baker and William Haynes
Colorado State University via Engineeringstatics

Key Questions

What are some strategies to practice selecting a tool from your problem-solving toolbox?
What is the basic problem-solving process for equilibrium?

Statics may be the first course you take where you are required to decide on your own how to approach a problem. Unlike your previous physics courses, you can't just memorize a formula and plug-and-chug to get an answer; there are often multiple ways to solve a problem, not all of them equally easy, so before you begin you need a plan or strategy. This seems to cause a lot of students difficulty.

The ways to think about forces, moments and equilibrium, and the mathematics used to manipulate them are like tools in your toolbox. Solving statics problems requires acquiring, choosing, and using these tools. Some problems can be solved with a single tool, while others require multiple tools. Sometimes one tool is a better choice, sometimes another. You need familiarity and practice to get skilled using your tools. As your skills and understanding improve, it gets easier to recognize the most efficient way to get a job done.

Struggling statics students often say things like:

“I don't know where to start the problem.” “It looks so easy when you do it.” “If I only knew which equation to apply, I could solve the problem.”

These statements indicate that the students think they know how to use their tools, but are skipping the planning step. They jump right to writing equations and solving for things without making much progress towards the answer, or they start solving the problem using a reasonable approach but abandon it in mid-stream to try something else. They get lost, confused and give up.

Choosing a strategy gets easier with experience. Unfortunately, the way you get that experience is to solve problems. It seems like a chicken and egg problem and it is, but there are ways around it. Here are some suggestions which will help you become a better problem-solver.

Get fluent with the math skills from algebra and trigonometry.
Do lots of problems, starting with simple ones to build your skills.
Study worked out solutions, however don't assume that just because you understand how someone else solved a problem that you can do it yourself without help.
Solve problems using multiple approaches. Confirm that alternate approaches produce the same results, and try to understand why one method was easier than the other.
Draw neat, clear, labeled diagrams.
Familiarize yourself with the application, assumptions, and terminology of the methods covered in class and the textbook.
When confused, identify what is confusing you and ask questions.

The majority of the topics in this book focus on equilibrium. The remaining topics are either preparing you for solving equilibrium problems or setting you up with skills that you will use in later classes. For equilibrium problems, the problem-solving steps are:

1. Read and understand the problem.

2. Identify what you are asked to find and what is given.

3. Stop, think, and decide on an strategy.

4. Draw a free-body diagram and define variables.

5. Apply the strategy to solve for unknowns and check solutions.

6. a. Write equations of equilibrium based on the free-body diagram.

b. Check if the number of equations equals the number of unknowns. If it doesn’t, you are missing something. You may need additional free-body diagrams or other relationships.

c. Solve for unknowns.

7. Conceptually check solutions.

Using these steps does not guarantee that you will get the right solution, but it will help you be critical and conscious of your chosen strategies. This reflection will help you learn more quickly and increase the odds that you choose the right tool for the job.

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Chapter 1: Fundamental Concepts

1.7 Problem Solving Process

Learning how to use a structured problem solving process will help you to be more organized and support your future courses. Also, it will train your brain how to approach problems. Just like basketball players practice jump shots over and over to train their body how to act in high pressure scenarios, if you are comfortable and familiar with a structured problem solving process, when you’re in a high pressure situation like a test, you can just jump into the problem like muscle memory.

6 Step Problem Solving Method:

Write out the answer with all necessary information that is given to you. It feels like it takes forever, but it’s important to have the problem and solution next to each other.
Draw the problem, this is usually a free-body diagram (don’t forget a coordinate frame). Eventually, as you get further into the course, you might need a few drawings. One would be a quick sketch of the problem in the real world, then modelling it into a simplified engineering drawing, and finally the free-body diagram.
Write out a list of the known/given values with the variable and unit, i.e m = 14 kg (variable = number unit)
Write out a list of the unknown values that you will have to solve for in order to solve the problem
You can also add any assumptions you made here that change the problem.
Also state any constants, i.e. g = 32.2 ft/m 2 or g = 9.81 m/s 2
This step helps you to have all of the information in one place when you solve the problem. It’s also important because each number should include units, so you can see if the units match or if you need to convert some numbers so they are all in English or SI. This also gives you the variables side by side to ensure they are unique (so you don’t accidentally have 2 ‘d’ variables and can rename one with a subscript).
Write a simple sentence or phrase explaining what method/approach you will be using to solve the problem.
For example: ‘use method of joints’, or equilibrium equations for a rigid body, MMOI for a certain shape, etc.
This is going to be more important when you get to the later chapters and especially next semester in Dynamics where you can solve the same problem many ways. Might as well practice now!
This is the actual solving step. This is where you show all the work you have done to solve the problem.
When you get an answer, restate the variable you are solving for, include the unit, and put a box around the answer.
Write a simple sentence explaining why (or why not) your answer makes sense. Use logic and common sense for this step.
When possible, use a second quick numerical analysis to verify your answer. This is the “gut check” to do a quick calculation to ensure your answer is reasonable.
This is the most confusing step as students often don’t know what to put here and up just writing ‘The number looks reasonable’. This step is vitally important to help you learn how to think about your answer. What does that number mean? What is it close to? For example, if you find that x = 4000 m, that’s a very large distance! In the review, I would say, ‘the object is 4 km long which is reasonable for a long bridge’. See how this is compared to something similar? Or you could do a second calculation to verify the number is correct, such as adding up multiple parts of the problem to confirm the total length is accurate i.e. ‘x + y + z = total, yes it works!’

Additional notes for this course:

It’s important to include the number and label the steps so it’s clear what you’re doing, as shown in the example below.
It’s okay if you make mistakes, just put a line through it and keep going.
Remember your header should include your name, the page number, total number of pages, the course number, and the assignment number. If a problem spans a number of pages, you should include it in the header too.

Key Takeaways

Basically: Use a 6-step structured problem solving process: 1. Problem, 2. Draw, 3. Known & Unknown, 4. Approach, 5. Analysis (Solve), 6. Review

Application: In your future job there is likely a structure for analysis reports that will be used. Each company has a different approach, but most have a standard that should be followed. This is good practice.

Looking ahead: This will be part of every homework assignment.

Written by Gayla & Libby

Engineering Mechanics: Statics Copyright © by Libby (Elizabeth) Osgood; Gayla Cameron; Emma Christensen; Analiya Benny; and Matthew Hutchison is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Tips for Solving Engineering Problems Effectively

Problem solving is the process of determining the best feasible action to take in a given situation. Problem solving is an essential skill for engineers to have. Engineers are problem solvers, as the popular quote says:

“Engineers like to solve problems. If there are no problems handily available, they will create their own problems.” – Scott Adams

Engineers are faced with a range of problems in their everyday life. The nature of problems that engineers must solve differs between and among the various disciplines of engineering. Because of the diversity of problems there is no universal list of procedures that will fit every engineering problem. Engineers use various approaches while solving problems.

Engineering problems must be approached systematically, applying an algorithm, or step-by-step practice by which one arrives at a feasible solution. In this post, we’ve prepared a list of tips for solving engineering problems effectively.

#1 Identify the Problem

Evaluating the needs or identifying the problem is a key step in finding a solution for engineering problems. Recognize and describe the problem accurately by exploring it thoroughly. Define what question is to be answered and what outputs or results are to be produced. Also determine the available data and information about the problem in hand.

An improper definition of the problem will cause the engineer to waste time, lengthen the problem solving process and finally arrive at an incorrect solution. It is essential that the stated needs be real needs.

As an engineer, you should also be careful not to make the problem pointlessly bound. Placing too many limitations on the problem may make the solution extremely complex and tough or impossible to solve. To put it simply, eliminate the unnecessary details and only keep relevant details and the root problem.

#2 Collect Relevant Information and Data

After defining the problem, an engineer begins to collect all the relevant information and data needed to solve the problem. The collected data could be physical measurements, maps, outcomes of laboratory experiments, patents, results of conducted surveys, or any number of other types of information. Verify the accuracy of the collected data and information.

As an engineer, you should always try to build on what has already been done before. Don’t reinvent the wheel. Information on related problems that have been solved or unsolved earlier, may help engineers find the optimal solution for a given problem.

#3 Search for Creative Solutions

There are a number of methods to help a group or individual to produce original creative ideas. The development of these new ideas may come from creativity, a subconscious effort, or innovation, a conscious effort.

You can try to visualize the problem or make a conceptual model for the given problem. So think of visualizing the given problem and see if that can help you gain more knowledge about the problem.

#4 Develop a Mathematical Model

Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application.

To develop a mathematical model for the problem, determine what basic principles are applicable and then draw sketches or block diagrams to better understand the problem. Then define and introduce the necessary variables so that the problem is stated purely in mathematical terms.

Afterwards, simplify the problem so that you can obtain the required result. Also identify the and justify the assumptions and constraints in the mathematical model.

#5 Use Computational Method

You can use a computational method based on the mathematical method you’ve developed for the problem. Derive a set of equations that enable the calculation of the desired parameters and variables as described in your mathematical model. You can also develop an algorithm, or step-by-step procedure of evaluating the equations involved in the solution.

To do so, describe the algorithm in mathematical terms and then execute it as a computer program.

#6 Repeat the Problem Solving Process

Not every problem solving is immediately successful. Problems aren’t always solved appropriately the first time. You’ve to rethink and repeat the problem solving process or choose an alternative solution or approach to solving the problem.

Bottom-line:

Engineers often use the reverse-engineering method to solve problems. For example, by taking things apart to identify a problem, finding a solution and then putting the object back together again. Engineers are creative , they know how things work, and so they constantly analyze things and discover how they work.

Problem-solving skills help you to resolve obstacles in a situation. As stated earlier, problem solving is a skill that an engineer must have and fortunately it’s a skill that can be learned. This skill gives engineers a mechanism for identifying things, figuring out why they are broken and determining a course of action to fix them.

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Solving Everyday Problems Using the Engineering Design Cycle

Hands-on Activity Solving Everyday Problems Using the Engineering Design Cycle

Grade Level: 7 (6-8)

(two 60-minutes class periods)

Additional materials are required if the optional design/build activity extension is conducted.

Group Size: 4

Activity Dependency: None

Subject Areas: Science and Technology

NGSS Performance Expectations:

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Engineering connection, learning objectives, materials list, worksheets and attachments, introduction/motivation, vocabulary/definitions, investigating questions, activity extensions, user comments & tips.

Engineers help design and create healthier tomorrows

This activity introduces students to the steps of the engineering design process. Engineers use the engineering design process when brainstorming solutions to real-life problems; they develop these solutions by testing and redesigning prototypes that work within given constraints. For example, biomedical engineers who design new pacemakers are challenged to create devices that help to control the heart while being small enough to enable patients to move around in their daily lives.

After this activity, students should be able to:

Explain the stages/steps of the engineering design process .
Identify the engineering design process steps in a case study of a design/build example solution.
Determine whether a design solution meets the project criteria and constraints.
Think of daily life situations/problems that could be improved.
Apply the engineering design process steps to develop their own innovations to real-life problems.
Apply the engineering design cycle steps to future engineering assignments.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science, international technology and engineering educators association - technology.

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State Standards

Massachusetts - science.

Each group needs:

Marisol Case Study , one per student
Group Leader Discussion Sheet , one per group

To share with the entire class:

computer/projector setup to show the class the Introduction to the Engineering Design Cycle Presentation , a Microsoft® PowerPoint® file
paper and pencils
(optional) an assortment of scrap materials such as fabric, super glue, wood, paper, plastic, etc., provided by the teacher and/or contributed by students, to conduct the hands-on design/build extension activity

(Have the 19-slide Introduction to the Engineering Design Cycle Presentation , a PowerPoint® file, ready to show the class.)

Have you ever experienced a problem and wanted a solution to it? Maybe it was a broken backpack strap, a bookshelf that just kept falling over, or stuff spilling out of your closet? (Let students share some simple problems with the class). With a little bit of creativity and a good understanding of the engineering design process, you can find the solutions to many of these problems yourself!

But what is the engineering design process? (Listen to some student ideas shared with the class.) The engineering design process, or cycle, is a series of steps used by engineers to guide them as they solve problems.

(Show students the slide presentation. Refer to the notes under each slide for a suggested script and comments. The slides introduce the main steps of the engineering design process, and walk through a classroom problem—a teacher’s disorganized desk that is preventing timely return of graded papers—and how students devise a solution. It also describes the work of famous people—Katherine Johnson, Lee Anne Walters, Marc Edwards, James E. West and Jorge Odón—to illustrate successful examples of using the steps of the engineering design process.)

Now that we’ve explore the engineering design process, let’s see if we can solve a real-world problem. Marisol is a high-school student who is very excited to have their own locker. They have lots of books, assignments, papers and other items that they keep in their locker. However, Marisol is not very organized. Sometimes they are late to class because they need extra time to find things that were stuffed into their locker. What is Marisol’s problem? (Answer: Their locker is disorganized.) In your groups, you’ll read through Marisol’s situation and see how they use the engineering design process to solve it. Let’s get started!

This activity is intended as an introduction to the engineering design cycle. It is meant to be relatable to students and serve as a jumping off point for future engineering design work.

Engineers follow the steps of the engineering design process to guide them as they solve problems. The steps shown in Figure 1 are:

Ask: identify the need & constraints

Identify and define the problem. Who does the problem affect? What needs to be accomplished? What is the overall goal of the project?
Identify the criteria and constraints. The criteria are the requirements the solution must meet, such as designing a bag to hold at least 10 lbs. Constraints are the limitations and restrictions on a solution, such as a maximum budget or specific dimensions.

Research the problem

Learn everything you can about the problem. Talk to experts and/or research what products or solutions already exist.
If working for a client, such as designing new filters for a drinking water treatment plant, talk with the client to determine the needs and wants.

Imagine: develop possible solutions

Brainstorm ideas and come up with as many solutions as possible. Wild and crazy ideas are welcome! Encourage teamwork and building on ideas.

Plan: select a promising solution

Consider the pros and cons of all possible solutions, keeping in mind the criteria and constraints.
Choose one solution and make a plan to move forward with it.

Create: build a prototype

Create your chosen solution! Push for creativity, imagination and excellence in the design.

Test and evaluate prototype

Test out the solution to see how well it works. Does it meet all the criteria and solve the need? Does it stay within the constraints? Talk about what worked during testing and what didn’t work. Communicate the results and get feedback. What could be improved?

Improve: redesign as needed

Optimize the solution. Redesign parts that didn’t work, and test again.
Iterate! Engineers improve their ideas and designs many times as they work towards a solution.

Some depictions of the engineering design process delineate a separate step—communication. In the Figure 1 graphic, communication is considered to be incorporated throughout the process. For this activity, we call out a final step— communicate the solution —as a concluding stage to explain to others how the solution was designed, why it is useful, and how they might benefit from it. See the diagram on slide 3.

For another introductory overview of engineering and design, see the What Is Engineering? What Is Design? lesson and/or show students the What Is Engineering? video.

Before the Activity

Make copies of the five-page Marisol Case Study , one per student, and the Group Leader Discussion Sheet , one per group.
Be ready to show the class the Introduction to the Engineering Design Cycle Presentation , a PowerPoint® file.

With the Students

As a pre-activity assessment, spend a few minutes asking students the questions provided in the Assessment section.
Present the Introduction/Motivation content to the class, which includes using the slide presentation to introduce students to the engineering design cycle. Throughout, ask for their feedback, for example, any criteria or constraints that they would add, other design ideas or modifications, and so forth.
Divide the class into groups of four. Ask each team to elect a group leader. Hand out the case study packets to each student. Provide each group leader with a discussion sheet.
In their groups, have students work through the case study together.
Alert students to the case study layout with its clearly labeled “stop” points, and direct them to just read section by section, not reading beyond those points.
Suggest that students either taking turns reading each section aloud or read each section silently.
Once all students in a group have read a section, the group leader refers to the discussion sheet and asks its questions of the group, facilitating a discussion that involves every student.
Encourage students to annotate the case study as they like; for example, they might note in the margins Marisol’s stage in the design process at various points.
As students work in their groups, walk around the classroom and encourage group discussion. Ensure that each group member contributes to the discussion and that group members are focused on the same section (no reading ahead).
After all teams have finished the case study and its discussion questions, facilitate a class discussion about how Marisol used the engineering design cycle. This might include referring back to questions 4 and 5 in “Stop 5” to discuss remaining questions about the case study and relate the case study example back to the community problems students suggested in the pre-activity assessment.
Administer the post-activity assessment.

brainstorming: A team creativity activity with the purpose to generate a large number of potential solutions to a design challenge.

constraint: A limitation or restriction. For engineers, design constraints are the requirements and limitations that the final design solutions must meet. Constraints are part of identifying and defining a problem, the first stage of the engineering design cycle.

criteria: For engineers, the specifications and requirements design solutions must meet. Criteria are part of identifying and defining a problem, the first stage of the engineering design cycle.

develop : In the engineering design cycle, to create different solutions to an engineering problem.

engineering: Creating new things for the benefit of humanity and our world. Designing and building products, structures, machines and systems that solve problems. The “E” in STEM.

engineering design process: A series of steps used by engineering teams to guide them as they develop new solutions, products or systems. The process is cyclical and iterative. Also called the engineering design cycle.

evaluate: To assess something (such as a design solution) and form an idea about its merit or value (such as whether it meets project criteria and constraints).

optimize: To make the solution better after testing. Part of the engineering design cycle.

Pre-Activity Assessment

Intro Discussion: To gauge how much students already know about the activity topic and start students thinking about potential design problems in their everyday lives, facilitate a brief class discussion by asking students the following questions:

What do engineers do? (Example possible answers: Engineers design things that help people, they design/build/create new things, they work on computers, they solve problems, they create things that have never existed before, etc.)
What are some problems in your home, school or community that could be solved through engineering? (Example possible answers: It is too dark in a community field/park at night, it is hard to carry shopping bags in grocery store carts, the dishwasher does not clean the dishes well, we spend too much time trying to find shoes—or other items—in the house/garage/classroom, etc.)
How do engineers solve problems? (Example possible answers: They build new things, design new things, etc. If not mentioned, introduce students to the idea of the engineering design cycle. Liken this to how research scientists are guided by the steps of the scientific method.)

Activity Embedded Assessment

Small Group Discussions: As students work, observe their group discussions. Make sure the group leaders go through all the questions for each section, and that each group member contributes to the discussions.

Post-Activity Assessment

Marisol’s Design Process: Provide students with writing paper and have them write “Marisol’s Design Process” at the top. Direct them to clearly write out the steps that Marisol went through as they designed and completed their locker organizer design and label them according to where they fit in the engineering design cycle. For example, “Marisol had to jump back to avoid objects falling out of their locker” and they stated a desire to “wanted to find a way to organize their locker” both illustrate the “identifying the problem” step.

Which part of the engineering design cycle is Marisol working on as they design an organizer?
Why is it important to identify the criteria and constraints of a project before building and testing a prototype? (Example possible answers: So that the prototype will be the right size, so that you do not go over budget, so that it will solve the problem, etc.)
Why do engineers improve and optimize their designs? (Example possible answers: To make it work better, to fix unexpected problems that come up during testing, etc.)

To make this a more hands-on activity, have students design and build their own locker organizers (or other solutions to real-life problems they identified) in tandem with the above-described activity, incorporating the following changes/additions to the process:

Before the activity: Inform students that they will be undertaking an engineering design challenge. Without handing out the case study packet, introduce students to Marisol’s problem: a disorganized locker. Ask students to bring materials from home that they think could help solve this problem. Then, gather assorted materials (wood and fabric scraps, craft materials, tape, glue, etc.) to provide for this challenge, giving each material a cost (for example, wood pieces cost 50¢, fabric costs 25¢, etc.) and write these on the board or on paper to hand out to the class.
Present the Introduction/Motivation content and slides to introduce students to the engineering design process (as described above). Then have students go through the steps of the engineering design process to create a locker organizer for Marisol. Inform them Marisol has only $3 to spend on an organizer, so they must work within this budget constraint. As a size constraint, tell students the locker is 32 inches tall, 12 inches wide and 9.5 inches deep. (Alternatively, have students measure their own lockers and determine the size themselves.)
As students work, ask them some reflection questions such as, “Which step of the engineering design process are you working on?” and “Why have you chosen that solution?”
Let groups present their organizers to the class and explain the logic behind their designs.
Next, distribute the case study packet and discussion sheets to the student groups. As the teams read through the packet, encourage them to discuss the differences between their design solutions and Marisol’s. Mention that in engineering design there is no one right answer; rather, many possible solutions may exist. Multiple designs may be successful in imagining and fabricating a solution that meets the project criteria and constraints.

Engineering Design Process . 2014. TeachEngineering, Web. Accessed June 20, 2017. https://www.teachengineering.org/k12engineering/designprocess

Contributors

Supporting program, acknowledgements.

This material is based upon work supported by the National Science Foundation CAREER award grant no. DRL 1552567 (Amy Wilson-Lopez) titled, Examining Factors that Foster Low-Income Latino Middle School Students' Engineering Design Thinking in Literacy-Infused Technology and Engineering Classrooms. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Last modified: October 26, 2023

Problem Identification in Engineering Design

Problem identification is the first step of the engineering problem solving method. The relevant themes, processes and techniques for electrical engineering and their application to the senior design project are presented here.

Theory and Background

Engineering is a profession of applied science. Engineers must creatively find new ways to solve problems, and are always real-world problems. As a result, they are usually more complex than most problems studied in school, since many of the assumptions that are made to illustrate a concept are no longer valid. Yet, engineers still must come up with some solution. With so many new factors to consider when forming a solution, the entire process may seem daunting. In this way, one of the most critical steps in the problem solving process is solid problem identification. By effectively identifying the exact problem, and engineer may limit his or her focus to only the factors required to solve that problem (Shaw, 2001).

When inexperienced students go about the problem solving process, there are several paths they might take. For example, suppose students are building some type of robot. They have wired all their circuits together, but upon testing the robot, it simply does not work. The worst path they could take in this problem solving situation is to place all the blame upon factors out of their control. “The wires we have are faulty, so there is nothing we can do.” While this might be the case, it should be the last resort, as it leads to giving up on all prior work.

More motivated students might check several parts of their design and tinker with it until it works. This ad-hoc method is most common. The students can recall different ideas they have heard might cause problems, and check each one sequentially until a solution is found. In this manner, the problem identification is melded directly to the solution, as finding the latter leads to discovering the former. The difficulty with this ad-hoc method is that it varies with each project, so a more general system to fix problems cannot be extracted from this.

The best students may look at generalized problem solving methods that have been studied and improved upon for decades, and find a way to apply it to their project. This is the path that we will examine, and to do so, we will look at several example methods.

Common Themes

The similarities among the problem solving methods can be seen across many industries, especially business. Even with no scientific or technical aspects to a situation, the same ideas identify the problems effectively. One main cause for the similarities is the desire in business and other fields to have a rigorous methodology aimed at improving the target idea, project, company, etc.

To look at some common themes in problem solving methods, we will compare four widely used techniques: the TRIZ method, Root Cause Failure Analysis, and the two methods described in How to Solve It by Pólya (1957).

TRIZ Method

TRIZ, which is a Russian acronym for Theory of Inventive Problem Solving , is a problem solving method based on the study of patterns in problems and solutions. The developers of this method have analyzed over three million inventions with the intent of predicting where breakthroughs will come from (Jugulum & Samuel, 2008). The idea is that problems and solutions are repeated across a wide variety of applications, so by generalizing the problem, one can find a proven solution. Once the abstracted problem has been solved, the solution must then be adapted to the specific situation.

This method, like many other problem solving methods, is an iterative process. Identifying the problem is the first step. Once all the TRIZ analysis tools have been used and a solution has been identified, the process cycles back to identification again. Any new factors that arise from the initial solution must be addressed and attacked in the same manner as the original situation.

The main tool of classical TRIZ analysis for problem definition is the contradiction matrix. The axes of the matrix are engineering parameters, and potential general solutions are filled in the boxes. When one solution leads to a larger problem, a contradiction is identified. Kutz describes the tool:

The objective of the matrix is to direct the problem-solving process to incorporate an idea that has been utilized before to solve an analogous ‘‘inventive’’ problem. The contradiction matrix accomplishes this by asking two simple questions: Which element of the system is in need of improvement? If improved, which element of the system is deteriorated?” (Kutz, 2006, p. 622)

This is a useful tool if the design process is certain to be a long and iterative one. By going through such exhaustive planning and searching in the beginning, one can cut down many iterations in the process. However, the tool falls short if the scope is problem. It simply may not be necessary to write out the entire matrix for a problem that has only a few clear parameters to it.

Root Cause Failure Analysis

In reliability engineering and quality control, the main objective is to deal with problems and failures. It seems clear that a systematic approach to identifying the problem would arise in this field. This is the aim of Root Cause Failure Analysis (RFCA) (Mobley, 1999). The main idea is to identify the root cause of the problem that arises and eliminate it, as opposed to waiting for effects and mitigating them. It is analogous to getting vaccinated for the flu instead of waiting to catch it and then buying tissues.

There are several analysis techniques used in RFCA. These include Failure Mode and Effects Analysis, Cause and Effect Analysis, also known as fishbone analysis, and Sequence of Events Analysis. The applicability of each technique depends on what type of problem is present and what you want to focus on. For example, when the problem arose over time, the sequence analysis might be best. Alternatively, when you just want to lay out all possible causes without giving weight to any, the fishbone analysis is useful. A diagram of fishbone analysis is shown in Figure 1.

Fishbone Analysis.

The main issue unique to RFCA is the high cost of performing such an analysis (Mobley,1999). This means it should be used only when it is absolutely necessary. Also, it is somewhat limited in scope, as it was originally designed for use in chemical plant analysis.

How to Solve It

The book How to Solve It , written in 1957 by mathematician George Pólya, gives the methods used to solve many math problems and abstracts them to general problems. He generally describes the steps as understanding the problem, making a plan, carrying it out, and analyzing.

One of the most useful ideas he puts forth that is widely used in mathematics is to find an analogous problem and solve it. This is more useful in the extremely abstract world of mathematics where assumptions always hold true and objects are perfect, but the technique can be used to get a good approximation of a real world problem. In the world of engineering, this may be sufficient to get the job done.

While the techniques outlined in the book are very interesting to me as a mathematician, there are times when the methods can fall short. It is good practice to see how rigorous problem identifications and solutions can be generalized, but that is the majority of what the method does. To go out and solve your specific problem, there are still many specific connections to be made.

Application to Senior Project

The problem identification process is critical to the senior design project’s success. Before any design, implementation, or even productive planning can be done, the central problems behind the project must be laid out. This process goes hand in hand with identifying customer specifications. It is always critical to know precisely what the customer wants; however, in the ECE senior design projects , where student have essentially no prior experience, this step should get special care. See Ulrich & Eppinger (2004) for more information on customer specifications.

Once the customer’s needs and desires have been finalized, the problem identification may begin. There will almost certainly be multiple areas of the project that have a main problem. As you look at all the items the customer has suggested or demanded, you may find contradicting qualities. Here is where breaking the problem down to its most basic form is crucial. Only then can engineering decisions be made about which areas to compromise for the good of the whole project.

While the customer specification process only should occur once, the problem identification occurs many times as the design process is iterated. For example, in the Red Team’s senior project , which involved modifying a Parrot AR Drone toy helicopter to be able to autonomously collect data, the first major problem was finding usable and inexpensive hardware to add (Video 1). Once that had been solved, the next problem area was designing software that would allow the drone to hover stably at a target. Initially these two problems appeared to be the largest challenges; however, upon completing preliminary testing, it was discovered that no matter how sophisticated the stabilizing algorithm became, the helicopter would not remain very stable. As a result, the problem solving branched out in a direction previously unexpected. The process of identifying this new problem led to a workable solution.

The Red Team’s autonomous drone project navigating and gathering data. Source: Tufts SPARTN Channel on YouTube.com.

Cited References

Jugulum, R., & Samuel, P. (2008). Design for Lean Six Sigma – A Holistic Approach to Design and Innovation . Hoboken: John Wiley & Sons. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/637224080
Kutz, M. (2006). Mechanical Engineers’ Handbook – Materials and Mechanical Design (3rd ed.). Hoboken: John Wiley & Sons. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/59003354
Mobley, R.K. (1999). Root Cause Failure Analysis . Boston: Newnes/Elsevier. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/40255833
Pólya, G. (1957). How to Solve It . Garden City, NY: Doubleday. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/523312
Shaw, M. C. (2001). Engineering Problem Solving – A Classical Perspective . Norwich: William Andrew Publishing/Noyes. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/633151037

Additional Sources / Recommended Reading

Ulrich, K. T. & Eppinger, S. D. (2004). Product Design and Development . Boston/New York: McGraw-Hill/ Irwin. OCLC WorldCat Permalink: http://www.worldcat.org/oclc/122424997
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35 problem-solving techniques and methods for solving complex problems

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How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

Problem-solving techniques to identify and analyze problems
Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve.

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward.

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.

Try different approaches

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

Six Thinking Hats
Lightning Decision Jam
Problem Definition Process
Discovery & Action Dialogue

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on.

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages.

Lightning Decision Jam (LDJ) #action #decision making #problem solving #issue analysis #innovation #design #remote-friendly The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design.

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition #problem solving #idea generation #creativity #online #remote-friendly A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges.

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results.

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys #hyperisland #innovation This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold.

World Cafe #hyperisland #innovation #issue analysis World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD) #idea generation #liberating structures #action #issue analysis #remote-friendly DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology #action plan #idea generation #problem solving #issue analysis #large group #online #remote-friendly Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

The Creativity Dice
Fishbone Analysis
Problem Tree
SWOT Analysis
Agreement-Certainty Matrix
The Journalistic Six
LEGO Challenge
What, So What, Now What?
Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed.

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It! #gamestorming #problem solving #action Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed.

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable.

The Creativity Dice #creativity #problem solving #thiagi #issue analysis Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around.

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish.

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis #problem solving ##root cause analysis #decision making #online facilitation A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them.

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree #define intentions #create #design #issue analysis A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward.

SWOT analysis #gamestorming #problem solving #action #meeting facilitation The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results.

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause.

Agreement-Certainty Matrix #issue analysis #liberating structures #problem solving You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic . A problem is simple when it can be solved reliably with practices that are easy to duplicate. It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably. A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail. Chaotic is when the context is too turbulent to identify a path forward. A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.” The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process.

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID #gamestorming #project planning #issue analysis #problem solving When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!

Speed Boat #gamestorming #problem solving #action Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How #idea generation #issue analysis #problem solving #online #creative thinking #remote-friendly A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills.

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO!

LEGO Challenge #hyperisland #team A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems.

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken.

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What? #issue analysis #innovation #liberating structures You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists #vision #big picture #issue analysis #remote-friendly This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

Improved Solutions
Four-Step Sketch
15% Solutions
How-Now-Wow matrix
Impact Effort Matrix

21. Mindspin

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly.

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation.

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex.

MindSpin #teampedia #idea generation #problem solving #action A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result.

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution.

Improved Solutions #creativity #thiagi #problem solving #action #team You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged.

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch #design sprint #innovation #idea generation #remote-friendly The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper, Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change.

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change.

15% Solutions #action #liberating structures #remote-friendly You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference. 15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change. With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process.

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud.

How-Now-Wow Matrix #gamestorming #idea generation #remote-friendly When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice.

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them.

Impact and Effort Matrix #gamestorming #decision making #action #remote-friendly In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action?

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus.

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively.

Dotmocracy #action #decision making #group prioritization #hyperisland #remote-friendly Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

Check-in/Check-out
Doodling Together
Show and Tell
Constellations
Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute.

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out #team #opening #closing #hyperisland #remote-friendly Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start.

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems.

Doodling Together #collaboration #creativity #teamwork #fun #team #visual methods #energiser #icebreaker #remote-friendly Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team!

Show and Tell #gamestorming #action #opening #meeting facilitation Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible.

Constellations #trust #connection #opening #coaching #patterns #system Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic.

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree #thiagi #opening #perspectives #remote-friendly With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space.

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round.

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them.

One breath feedback #closing #feedback #action This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward.

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved.

Who/What/When Matrix #gamestorming #action #project planning With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out!

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised.

Response Cards #debriefing #closing #structured sharing #questions and answers #thiagi #action It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks to build your agenda. When you make changes or update your agenda, your session timing adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore how to use SessionLab to design effective problem solving workshops or watch this five minute video to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you!

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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Physics > Physics Education

Title: real-world problem-solving class is correlated with higher student persistence in engineering.

Abstract: Student persistence in science, technology, engineering, and mathematics (STEM) has long been a focus of educational research, with both quantitative and qualitative methods being used to investigate patterns and mechanisms of attrition. Some studies have used machine learning to predict a student's likelihood to persist given measurable classroom factors and institutional data, while others have framed persistence as a function of a student's social integration in the classroom. While these methods have provided insight into broader underlying patterns of attrition in STEM, they have not investigated class structures or teaching methods that promote persistence. In this study we explore how a research-based instructional format for an introductory calculus-based physics class using real world problem-solving (RPS) was correlated with higher persistence for students at a large research-intensive university. We found that the one-year persistence rates for the RPS course were 74% (fall semester) and 90% (spring semester), while the lecture-based class had a persistence rate of 64% and 78%, respectively. In spring, the RPS persistence rate was significantly higher (p=0.037). The RPS also had higher final grades and larger learning gains than the lecture-based class despite lower scores on a physics diagnostic test. We also note that the higher rates of persistence were not completely explained by higher final grades. This study motivates future work to understand the structural mechanisms that promote student persistence in introductory physics courses.

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A multiscale stabilized physics informed neural networks with weakly imposed boundary conditions transfer learning method for modeling advection dominated flow

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Published: 06 May 2024

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Tsung-Yeh Hsieh 1 &
Tsung-Hui Huang ORCID: orcid.org/0000-0002-9582-8438 1

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Physics informed neural network (PINN) frameworks have been developed as a powerful technique for solving partial differential equations (PDEs) with potential data integration. However, when applied to advection based PDEs, PINNs confront challenges such as parameter sensitivity in boundary condition enforcement and diminished learning capability due to an ill-conditioned system resulting from the strong advection. In this study, we present a multiscale stabilized PINN formulation with a weakly imposed boundary condition (WBC) method coupled with transfer learning that can robustly model the advection diffusion equation. To address key challenges, we use an advection-flux-decoupling technique to prescribe the Dirichlet boundary conditions, which rectifies the imbalanced training observed in PINN with conventional penalty and strong enforcement methods. A multiscale approach under the least squares functional form of PINN is developed that introduces a controllable stabilization term, which can be regarded as a special form of Sobolev training that augments the learning capacity. The efficacy of the proposed method is demonstrated through the resolution of a series of benchmark problems of forward modeling, and the outcomes affirm the potency of the methodology proposed.

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Error estimates and physics informed augmentation of neural networks for thermally coupled incompressible Navier Stokes equations

Weight initialization algorithm for physics-informed neural networks using finite differences

A Review of Physics Informed Neural Networks for Multiscale Analysis and Inverse Problems

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The research data associated with this paper is not open to the public due to the policy of the author’s affiliation. Data requests can be made to the corresponding author of this research paper.

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Acknowledgements

This study was supported by the National Science and Technology Council, NSTC (formerly Ministry of Science and Technology, MOST), Taiwan, under project contract number 109-2222-E-007-005-MY3. The author T.H. Huang is additionally supported by NSTC project contract number 112-2628-E-007-018 and 112-2221-E-007-028. We would also like to acknowledge the research suggestions from Prof. Wei-Fan Hu at National Central University and Prof. Yi-Ju Chou at National Taiwan University. The author would like to appreciate the anonymous reviewers for their comments and suggestions for improving the quality of this work.

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1.1 Weights normalization for penalty method

To normalize the penalty parameter in the PINN, we run the dimension analysis for the loss function, by setting $u$ as the concentration field with the SI unit ${\text{mol}}/{{\text{m}}}^{3}$ , ${a}_{i}$ as advection velocity vector component with SI unit ${\text{m}}/{\text{s}}$ and diffusivity coefficient $k$ with SI unit ${{\text{m}}}^{2}/{\text{s}}$ . Here ${\text{mol}}$ indicates the mole number, ${\text{m}}$ indicates the unit meter and ${\text{s}}$ indicate the unit second. To satisfy dimension consistency, all terms in the loss function in Eq. ( 10 ) should results in same units eventually.

The unit of equilibrium equation loss ${\Pi }_{S}$ is shown below.

where ${\text{O}}\left(\cdot \right)$ means the order of the argument. Similarly, the Dirichlet boundary condition and Neumann boundary condition loss can be represented as:

Then, in order to enforce dimension consistency between Eqs. ( 56 )–( 58 ), the penalty parameter ${\beta }_{D}$ and ${\beta }_{N}$ can be normailized by the Peclet number, diffusivity coefficient and the characteristic length ${L}_{c}$ :

In the numerical testing, we then can define the following penalty parmeter by introducing a unitless coefficient ${\widehat{\beta }}_{D}$ and ${\widehat{\beta }}_{N}.$

1.2 Weights normalization for weakly enforced boundary condition method

By performing the dimension analysis for the WBC formulation for the two terms shown in Eq. ( 32 ), one obtains:

Then by comparing Eqs. ( 63 ) and ( 64 ) with the loss of the equilibrium Eq. ( 56 ), the dimension of the two parameters ${C}_{a}$ and ${C}_{k}$ can be expressed in terms of the Peclet number, diffusivity coefficient and the characteristic length ${L}_{c}$ :

Then, following the same logic shown in Eqs. ( 59 ) and ( 60 ), one can introduce controllable unitless coefficients ${\widehat{C}}_{a}$ and ${\widehat{C}}_{k}$ to represent ${C}_{a}$ and ${C}_{k}$

1.3 Influence of weights normalization effect for penalty method and WBC approach

The one-dimensional boundary layer problem in Sect. 2.3.1.1 is given below in Fig. 32 to perform the parameter study for both the penalty method and the WBC method. First, we select four choices of penalty parameters ${\widehat{\beta }}_{D}=0.01, 0.1, 1, 100$ ( ${\widehat{\beta }}_{D}=100.0$ is corresponding to unnormalized parameter ${\beta }_{D}=2.5\times {10}^{5}$ , which is a large enough value to impose boundary condition) for the penalty method. It can be seen that without the WBC approach, non-convergence result is found for Peclet number equaling 100 (advection dominate case). Secondly, we perform the same study for WBC method ${\widehat{C}}_{a}={\widehat{C}}_{k}=0.01, 0.1, 1$ in comparison to an improper choice of parameter ${\widehat{C}}_{a}={\widehat{C}}_{k}=100.0$ (corresponding to unnormalized parameter ${C}_{a}={C}_{k}=2.5\times {10}^{5}$ , making it large enough which make it similar to the penalty method). From the analysis, the value of ${\widehat{C}}_{a}={\widehat{C}}_{k}=100.0$ causes non-convergence solution in the $Pe=100$ case, while all other choices robustly capture the boundary layer feature. Therefore, we are assured that proper normalization is necessary for the WBC approach.

One-dimensional boundary layer problem with different ${\widehat{\beta }}_{D},{\widehat{C}}_{a},{\widehat{C}}_{k}$ selection in penalty and WBC methods

1.4 Coefficient sensitivity analysis of the penalty parameter in WBC fine-tuning

This analysis is conducted to investigate the effect of penalty coefficient ${\gamma }_{D}$ selection in the WBC fine-tuning stage, providing a reasonable selection range as well as demonstrating the solution balancing phenomenon of pre-trained solution and Dirichlet boundary conditions as mentioned in Sect. 3.1 . The two-dimensional point source boundary layer problem in Sect. 2.3.1.2 with different penalty coefficients defined on the boundary are conducted and demonstrated in Fig. 33 . From the result, we can see that since the pre-trained model already captures the main features of the system (advection), the second term for Dirichlet boundary condition regularization is not sensitive to the penalty coefficient ${\gamma }_{D}$ anymore. However, employing an excessively large penalty coefficient will lead to oscillation in the result as shown in Fig. 33 d and therefore a reasonable range ${\gamma }_{D}\in \left[\mathrm{0,1}\right]$ is recommended.

Two-dimensional point source boundary layer problem with different fine-tuning penalty coefficients

1.5 Numerical comparison of the proposed VMS-PINN with gradient-enhanced PINN (gPINN)

A numerical example is conducted to investigate the effect of parameter “ ${c}_{VMS}$ ” in Eq. ( 47 ) and VMS compared to the gPINN method [ 46 ]. The two-dimensional point source boundary layer problem (in Sect. 2.3.1.2 ) is used with all numerical setting remaining the same. The ${L}_{2}$ error norm in the training process is shown in Fig. 34 , and both gPINN and VMS methods use 50,000 iterations for training. The gPINN implemented in this numerical example employs a loss function accordinig to [ 46 ], as shown in Eq. ( 69 ):

where ${\mathcal{L}}_{{g}_{{\varvec{x}}}}$ and ${\mathcal{L}}_{{g}_{t}}$ are the gradient loss with respect to space and time and uses a penalty parameter $w=1.0$ according to the reference [ 46 ]. In this example, ${\mathcal{L}}_{{g}_{t}}$ is omitted since the problem is time independent. From the result, we can see that under the same experiment setting, the VMS has higher convergency compared with the gPINN result. It is possible that by optimal choice of the weight in the VMS gradient regularization term leads to a better result.

Numerical comparison of the proposed VMS method and the gradient enhanced PINN (gPINN) formulation in [ 46 ]. Both methods conduct 50,000 iterations of training

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Hsieh, TY., Huang, TH. A multiscale stabilized physics informed neural networks with weakly imposed boundary conditions transfer learning method for modeling advection dominated flow. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-01981-5

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What is Problem Solving?
Problem solving is a process. Most strategies provide steps that help you identify the problem and choose the best solution. There are two basic types of strategies: algorithmic and heuristic. Algorithmic strategies are traditional step-by-step guides to solving problems.
Engineering Design Process
The engineering design process emphasizes open-ended problem solving and encourages students to learn from failure. This process nurtures students' abilities to create innovative solutions to challenges in any subject! The engineering design process is a series of steps that guides engineering teams as we solve problems.
Engineering Method
The engineering method (design) is a systematic approach used to support an engineer or project team in reaching the desired solution to a problem, which has been specified by customers, sponsors, or stakeholders who perceive value in resolving the problem. Figure 1. Engineering Method. Source: Ronald L. Lasser
1.4: Problem Solving
For equilibrium problems, the problem-solving steps are: 1. Read and understand the problem. 2. Identify what you are asked to find and what is given. 3. Stop, think, and decide on an strategy. 4. Draw a free-body diagram and define variables.
The Engineering Method: A Step-by-Step Process for Solving Challenging
We created The Engineering Method, a simple set of steps that can help you break a problem down, find a path toward a solution, and avoid mistakes. Here at Formation, we apply the method to software engineering problems, but the same steps can be applied to many different fields. Step 1: Thoroughly understand the problem A. Ask clarifying questions
1.7 Problem Solving Process
Basically: Use a 6-step structured problem solving process: 1. Problem, 2. Draw, 3. Known & Unknown, 4. Approach, 5. Analysis (Solve), 6. Review. Application: In your future job there is likely a structure for analysis reports that will be used. Each company has a different approach, but most have a standard that should be followed.
What is 8D? Eight Disciplines Problem Solving Process
The eight disciplines (8D) model is a problem solving approach typically employed by quality engineers or other professionals, and is most commonly used by the automotive industry but has also been successfully applied in healthcare, retail, finance, government, and manufacturing. The purpose of the 8D methodology is to identify, correct, and ...
Tips for Solving Engineering Problems Effectively
Repeat the Problem Solving Process. Not every problem solving is immediately successful. Problems aren't always solved appropriately the first time. You've to rethink and repeat the problem solving process or choose an alternative solution or approach to solving the problem. Bottom-line: Engineers often use the reverse-engineering method to ...
Methods to Solve Any Engineering Problem
There are three basic methods to solve any engineering methods. Analytical Methods. Numerical Methods. Experimental methods. 1. Analytical Methods: The analytical method is most widely used in curriculum study as well as used by industrial designers to solve the engineering problems. It is a classical approach which gives 100 % accurate results.
Methodologies for Problem Solving: An Engineering Approach
Methodologies for Problem Solving: An Engineering Approach by JAMES J. SHARP Professor and Chairman of Civil Engineering, Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John's, NF AIB 3X5 ... "the process of devising a system, component or process to meet desired needs, it is a decision making process ...
Solving Everyday Problems Using the Engineering Design Cycle
This activity introduces students to the steps of the engineering design process. Engineers use the engineering design process when brainstorming solutions to real-life problems; they develop these solutions by testing and redesigning prototypes that work within given constraints. For example, biomedical engineers who design new pacemakers are ...
Problem Identification in Engineering Design
Problem identification is the first step of the engineering problem solving method. The relevant themes, processes and techniques for electrical engineering and their application to the senior design project are presented here. Theory and Background. Engineering is a profession of applied science.
Process Engineering Problem Solving
About this book. Avoid wasting time and money on recurring plant process problems by applying the practical, five-step solution in Process Engineering Problem Solving: Avoiding "The Problem Went Away, but it Came Back" Syndrome. Combine cause and effect problem solving with the formulation of theoretically correct working hypotheses and find a ...
35 problem-solving techniques and methods for solving complex problems
The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it's common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. ...
Real-World Problem-Solving Class is Correlated with Higher Student
Student persistence in science, technology, engineering, and mathematics (STEM) has long been a focus of educational research, with both quantitative and qualitative methods being used to investigate patterns and mechanisms of attrition. Some studies have used machine learning to predict a student's likelihood to persist given measurable classroom factors and institutional data, while others ...
A multiscale stabilized physics informed neural networks ...
Physics informed neural network (PINN) frameworks have been developed as a powerful technique for solving partial differential equations (PDEs) with potential data integration. However, when applied to advection based PDEs, PINNs confront challenges such as parameter sensitivity in boundary condition enforcement and diminished learning capability due to an ill-conditioned system resulting from ...

10 Steps to Problem Solving for Engineers

The stages of problem solving like a pro:

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Engineering Problem Solving ¶

Steps in solving ‘real world’ engineering problems ¶

Defining problems collaboratively ¶

How ‘good’ a solution do you need ¶

Steps in solving well-defined engineering process problems, including textbook problems ¶

3 What is Problem Solving?

Developing Problem Solving Processes

what does problem solving look like?

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1.4: Problem Solving

Key Questions

1.7 Problem Solving Process

6 Step Problem Solving Method:

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Tips for Solving Engineering Problems Effectively

#1 Identify the Problem

#2 Collect Relevant Information and Data

#3 Search for Creative Solutions

#4 Develop a Mathematical Model

#5 Use Computational Method

#6 Repeat the Problem Solving Process

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Problem Identification in Engineering Design

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35 problem-solving techniques and methods for solving complex problems

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How do you identify problems?

Complete problem-solving methods

Problem-solving warm-up activities

Tips for more effective problem solving

Clearly define the problem

Don’t jump to conclusions

Try different approaches

Don’t take it personally

Get the right people in the room

Document everything

Bring a facilitator

Develop your problem-solving skills

Design a great agenda

1. Six Thinking Hats

2. Lightning Decision Jam

3. Problem Definition Process

4. The 5 Whys

5. World Cafe

6. Discovery & Action Dialogue (DAD)

7. Design Sprint 2.0

8. Open space technology

Techniques to identify and analyze problems

10. The Creativity Dice

11. Fishbone Analysis

12. Problem Tree

13. SWOT Analysis

14. Agreement-Certainty Matrix

16. Speed Boat

17. The Journalistic Six