1. Problem Solving

2. Introduction  Engineers need to be good at solving problems and making things  Road to solutions just as important as solution itself  All students need problem-solving skills for technological 21st century, engineers or not  Engineers need to be good at solving problems and making things  Road to solutions just as important as solution itself  All students need problem-solving skills for technological 21st century, engineers or not http://members.telering.at/pat/einstein.htm

3. Analytic and Creative Problem Solving  Analytic  Only one correct answer exists  “What’s in your toolbox”  Critical for decisions that may put the public at risk  Analytic  Only one correct answer exists  “What’s in your toolbox”  Critical for decisions that may put the public at risk  Creative  There is no single correct answer  “How you handle your tools”  Ability to see how a product could malfunction or be misapplied

4. List of Possible “Tools” for Solving Simple Problems  Look for a pattern  Construct a table  Consider possibilities systematically  Act it out  Make a model  Make a figure, graph, or drawing  Work backwards  Select appropriate notation  Restate problem in own words  Look for a pattern  Construct a table  Consider possibilities systematically  Act it out  Make a model  Make a figure, graph, or drawing  Work backwards  Select appropriate notation  Restate problem in own words

5. List of Possible “Tools” for Solving Simple Problems  Identify necessary, desired and given information  Write an open-ended sentence  Identify a sub-goal  First solve a simpler problem  Change your point of view  Check for hidden assumptions  Use a resource  Generalize  Identify necessary, desired and given information  Write an open-ended sentence  Identify a sub-goal  First solve a simpler problem  Change your point of view  Check for hidden assumptions  Use a resource  Generalize

6. List of Possible “Tools” for Solving Simple Problems  Check the solution; validate it  Find another way to solve the problem  Find another solution  Study the solution process  Discuss limitations  Get a bigger hammer  Sleep on it  Brainstorm  Involve others  Check the solution; validate it  Find another way to solve the problem  Find another solution  Study the solution process  Discuss limitations  Get a bigger hammer  Sleep on it  Brainstorm  Involve others

7. Many Strategies  Most people rely on two - three strategies  Get stuck when those do not work  Developing additional tools or methods will allow you to tackle problems effectively  Most people rely on two - three strategies  Get stuck when those do not work  Developing additional tools or methods will allow you to tackle problems effectively http://web.mit.edu/tetazoo/www/img/calvin/

8. Analytic Problem Solving Methods  Scientific Method  Define the problem  Gather the facts  Develop a hypothesis  Perform a test  Evaluate the results  Scientific Method  Define the problem  Gather the facts  Develop a hypothesis  Perform a test  Evaluate the results  Analytic Method  Define problem, make problem statement  Diagram and describe  Apply theory and equations  Simplify assumptions  Solve necessary problems  Verify accuracy to required level

9. Step 1: Problem Statement  Restate problem to be solved in your own words  Engineering challenges are large and complex  Critical to understand what you need to solve  Restate problem to be solved in your own words  Engineering challenges are large and complex  Critical to understand what you need to solve

10. Step 2: Description  Describe the problem and list all that is known  Formally writing down info helps sort what is needed and what is required  Diagrams or sketches aid in understanding problem  Describe the problem and list all that is known  Formally writing down info helps sort what is needed and what is required  Diagrams or sketches aid in understanding problem

11. Step 3: Theory  State explicitly the theory or equations needed  Starting with full equations and simplifying reduces the possibility of overlooking important factors  State explicitly the theory or equations needed  Starting with full equations and simplifying reduces the possibility of overlooking important factors

12. Step 4: Simplifying Assumptions  Assists in solving a problem in a timely and cost-effective manner  Record assumptions and how they simplify the problem  Conservative Assumptions  Introduces errors on safe side  Need to develop ability to answer:  “What problem am I solving?”  “How do I get the solution I need most efficiently?”  Assists in solving a problem in a timely and cost-effective manner  Record assumptions and how they simplify the problem  Conservative Assumptions  Introduces errors on safe side  Need to develop ability to answer:  “What problem am I solving?”  “How do I get the solution I need most efficiently?”

13. Step 5: Problem Solution  Can be done by hand or with computers  Document what is done when arriving to solutions with computers  Allows for finding errors quickly  Shows others what was done  Can be done by hand or with computers  Document what is done when arriving to solutions with computers  Allows for finding errors quickly  Shows others what was done

14. Step 6: Accuracy Verification  Engineers responsible for verifying accuracy of their own solutions  Be Sure of Standards!!  Engineers responsible for verifying accuracy of their own solutions  Be Sure of Standards!! NIST Helps Verify Accuracy of the World’s Best Rulers for Measuring Time and Frequency http://www.nist.gov/public_affairs/gallery/bestrulers.htm

15. Methods of Verification  Estimate the answer  Simplify problem and solve  Are answers consistent?  Compare with similar solutions  Compare to previous work  Ask a more experienced engineer to review the results  Compare to published literature on problem  Estimate the answer  Simplify problem and solve  Are answers consistent?  Compare with similar solutions  Compare to previous work  Ask a more experienced engineer to review the results  Compare to published literature on problem

16. Methods of Verification  Ask yourself if the results makes sense  Compare to your own experience  Repeat the calculation  Run a computer simulation or model  Redo the calculation backwards  Ask yourself if the results makes sense  Compare to your own experience  Repeat the calculation  Run a computer simulation or model  Redo the calculation backwards

17. Estimation  Provides answers to problems quickly and can verify complicated analyses  Experienced engineers can estimate close to actual answer before analysis  Have confidence in your results by developing tools to verify accuracy  Provides answers to problems quickly and can verify complicated analyses  Experienced engineers can estimate close to actual answer before analysis  Have confidence in your results by developing tools to verify accuracy

18. Creative Problem Solving  Dividing the process into steps allows you to break a large, complex problem into simpler problems where your various skills can be used  5 Questions for Creative Problem Solving  What is wrong?  What do we know?  What is the real problem?  What is the best solution?  How do we implement the solution?  Dividing the process into steps allows you to break a large, complex problem into simpler problems where your various skills can be used  5 Questions for Creative Problem Solving  What is wrong?  What do we know?  What is the real problem?  What is the best solution?  How do we implement the solution?

19. Divergence and Convergence  At each phase there is a divergent and convergent part of the process  Divergent Process  Start at one point and reach for as many ideas as possible  Quantity important  Identifying possibilities is the goal  Convergent Process  Analytical and evaluative tools used to narrow possibilities to one most likely to yield an answer  Quality is most important  Find best possibility to move the process to next phase  At each phase there is a divergent and convergent part of the process  Divergent Process  Start at one point and reach for as many ideas as possible  Quantity important  Identifying possibilities is the goal  Convergent Process  Analytical and evaluative tools used to narrow possibilities to one most likely to yield an answer  Quality is most important  Find best possibility to move the process to next phase

20. What is Wrong?  Identify an issue  Can be stated or determined on your own  May involve  Optimizing a process  Improving customer satisfaction  Addressing reliability issues

21. What do we know?  Gathering all facts and information related to problem identified  Do not evaluate whether the data are central to the problem  Gathering all facts and information related to problem identified  Do not evaluate whether the data are central to the problem

22. What is the the Real Problem?  Often skipped, but critical to effective solutions  Answers “Why”  Create a list of potential causes  Evaluate each to its validity  Rank each in order of impact http://www.rootsweb.com/~kscomanc/jordan.html

23. What is the Best Solution?  Potential solutions need to be generated  Wise to confer with experienced experts about problem’s solution  Go to more than 1 source  Most productive after list of causes generated http://www.nurp.noaa.gov/Spotlight%20Articles/g ashydrates.html

24. Implementing the Solution  Appropriate additional problems must be selected, done, and completed  Divergent Phase  Brainstorming  Convergent Phase  Selection of implementation plan  Appropriate additional problems must be selected, done, and completed  Divergent Phase  Brainstorming  Convergent Phase  Selection of implementation plan

25. Evaluating the Solution  Problem solving, just like design, is a cyclic process  Obtain a neutral view from someone not involved with formulation or solution process  Allows you to learn from the process and the solution  Reflection process  Problem solving, just like design, is a cyclic process  Obtain a neutral view from someone not involved with formulation or solution process  Allows you to learn from the process and the solution  Reflection process

26. Personal Problem- Solving Styles  Isaken and Treffinger Six Linear Steps  Dr. Min Basadur’s Simplex Model  Basadur Simplex Creative Problem- Solving Profile  Isaken and Treffinger Six Linear Steps  Dr. Min Basadur’s Simplex Model  Basadur Simplex Creative Problem- Solving Profile

27. Isaken and Treffinger Six Linear Steps  Mess Finding  Data Finding  Problem Finding  Idea Finding  Solution Finding  Acceptance Finding  Mess Finding  Data Finding  Problem Finding  Idea Finding  Solution Finding  Acceptance Finding

28. Dr. Min Basadur’s Simplex  Problem finding  Fact finding  Problem defining  Idea finding  Evaluating and selecting  Action planning  Gaining acceptance  Taking action  Problem finding  Fact finding  Problem defining  Idea finding  Evaluating and selecting  Action planning  Gaining acceptance  Taking action

29. Basadur Simplex Creative Problem-Solving Profile  Four styles, each correlating with 2 of the 8 of his Simplex model  Grouped into Quadrants  Q1 - Generator  Q2 - Conceptualizer  Q3 - Optimizer  Q4 - Implementor  Four styles, each correlating with 2 of the 8 of his Simplex model  Grouped into Quadrants  Q1 - Generator  Q2 - Conceptualizer  Q3 - Optimizer  Q4 - Implementor

30. Generating  Getting the problem-solving process rolling  Problem & fact finding  Direct Experience  Questioning  Imagining Possibilities  Sensing Problems and Opportunities  Viewing from different perspectives  Focus on creating options rather than evaluating  Getting the problem-solving process rolling  Problem & fact finding  Direct Experience  Questioning  Imagining Possibilities  Sensing Problems and Opportunities  Viewing from different perspectives  Focus on creating options rather than evaluating

31. Conceptualizing  Gaining understanding by abstract thinking  Keeps innovation process going  To them, a theory must be logically sound and precise  Problem and idea finding  Gaining understanding by abstract thinking  Keeps innovation process going  To them, a theory must be logically sound and precise  Problem and idea finding

32. Optimizing  Moves innovation process further  Converts abstract thinking into practical solutions and plans  Create optimal solutions to a few well- defined problems or issues  Idea evaluation, selection and action planning  Moves innovation process further  Converts abstract thinking into practical solutions and plans  Create optimal solutions to a few well- defined problems or issues  Idea evaluation, selection and action planning

33. Implementing  Completes the innovation process  Learning by direct experience  Prefer situations where they must get things to work  Gaining acceptance and implementing  Completes the innovation process  Learning by direct experience  Prefer situations where they must get things to work  Gaining acceptance and implementing

34. Your Creative Problem- Solving Style  Reflects your preferences for each of the quadrants  Teams require strength in all four quadrants to succeed in creative problem-solving  Skills in all four quadrants are equally valuable  Reflects your preferences for each of the quadrants  Teams require strength in all four quadrants to succeed in creative problem-solving  Skills in all four quadrants are equally valuable

35. Brainstorming Strategies  Goal of brainstorming is to stimulate your mind to trigger concepts or ideas that normal problem solving might miss  Let your mind wander and write down any ideas that come into your head  Goal of brainstorming is to stimulate your mind to trigger concepts or ideas that normal problem solving might miss  Let your mind wander and write down any ideas that come into your head

36. Alex Osborn’s List of Stimulating Words  Adapt  Put to other uses  Modify  Magnify  Minify  Substitute  Rearrange  Reverse  Combine  Adapt  Put to other uses  Modify  Magnify  Minify  Substitute  Rearrange  Reverse  Combine

37. Bob Eberle’s Modified Osborn List (SCAMPER)  Substitute?  Combine?  Adapt?  Modify? Minify? Magnify?  Put to other uses?  Eliminate?  Reverse? Rearrange?  Substitute?  Combine?  Adapt?  Modify? Minify? Magnify?  Put to other uses?  Eliminate?  Reverse? Rearrange?

38. Individual Brainstorming  Advantage of privacy  Write down any ideas that come into your head  Get everything down on paper in thumbnail sketches or drawings that capture the thinking  Advantage of privacy  Write down any ideas that come into your head  Get everything down on paper in thumbnail sketches or drawings that capture the thinking

39. Group Brainstorming  Same goal as Individual Brainstorming  Generate as many potential solutions as possible without judging any of them  Advantages  Additional people look at problem differently and bring fresh perspectives  Others get involved in the process early  Same goal as Individual Brainstorming  Generate as many potential solutions as possible without judging any of them  Advantages  Additional people look at problem differently and bring fresh perspectives  Others get involved in the process early

40. Guidelines in Using Group Brainstorming  Pick a facilitator  Define the problem  Select a small group  Explain the process  Record ideas  Pick a facilitator  Define the problem  Select a small group  Explain the process  Record ideas  Involve everyone  No evaluating  Eliminate duplicates  Pick three

41. Pick a Facilitator  Record ideas  Keeps team focused  Makes sure the ground rules of brainstorming are followed by everyone  Record ideas  Keeps team focused  Makes sure the ground rules of brainstorming are followed by everyone

42. Define the Problem  All participants understand the problem  Definition discussion occurs BEFORE brainstorming begins  Avoid distractions  Bring process to a halt  All participants understand the problem  Definition discussion occurs BEFORE brainstorming begins  Avoid distractions  Bring process to a halt

43. Select a Small Group  Manageable size  Limited to three people  Break larger groups into subsections and reconvene with separate ideas  Manageable size  Limited to three people  Break larger groups into subsections and reconvene with separate ideas

44. Explain the Process  Provide the details of the process group will follow  Participants feel comfort knowing what they are getting into  Provide the details of the process group will follow  Participants feel comfort knowing what they are getting into

45. Record Ideas  Visibly record all ideas for group to see  Semi-circle around recorder  Multiple senses stimulate more ideas  Record ALL ideas  Often the best ideas come from a trigger of a silly idea  Visibly record all ideas for group to see  Semi-circle around recorder  Multiple senses stimulate more ideas  Record ALL ideas  Often the best ideas come from a trigger of a silly idea

46. Involve Everyone  Start with one idea from facilitator or another volunteer and write down  Easier to start with something on page  Go around group quickly allowing each person to submit one idea  If a person draws a blank, pass and come back  Power lies in taking advantage of everyone’s creative minds  Start with one idea from facilitator or another volunteer and write down  Easier to start with something on page  Go around group quickly allowing each person to submit one idea  If a person draws a blank, pass and come back  Power lies in taking advantage of everyone’s creative minds

47. No Evaluating  Telling someone their idea is subpar will result in less ideas spoken from that individual and the group  Wacky ideas may trigger the final solution  Participants need to feel at ease when brainstorming  Avoiding negative comments and other subtle signs  Saying “good idea” to one and not the other  Telling someone their idea is subpar will result in less ideas spoken from that individual and the group  Wacky ideas may trigger the final solution  Participants need to feel at ease when brainstorming  Avoiding negative comments and other subtle signs  Saying “good idea” to one and not the other

48. Eliminate Duplicates  Examine list of all ideas  Eliminate repeated ideas  Examine list of all ideas  Eliminate repeated ideas

49. Pick Three  Have members evaluate each suggestion by selecting top three choices  Mark each choice  Do not number  Groups time is optimized and no one feels like their ideas were “Number 4”  Have members evaluate each suggestion by selecting top three choices  Mark each choice  Do not number  Groups time is optimized and no one feels like their ideas were “Number 4”