Statistics and experimental design


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  • What is TRIZ ? TRIZ is a Russian acronym meaning "Theory of Inventive Problem Solving". In 1946, Genrich Altshuller, the founder of TRIZ, was a patent reviewer at the Russian naval patent office at the young age of 20. He perceived that there is a definite pattern in the way innovations take place in technical systems. He started a study of 200,000 patents to look for the basic principles and patterns in the world's most innovative patents. He found that each of the most inventive patents primarily solved an ‘inventive’ problem. Altshuller defined inventive problems as those which contain conflicting requirements, which he called ‘contradictions’. Further he found that the same fundamental solutions were used over and over again, often separated by many years. He reasoned that if latter inventors had the knowledge of earlier solutions their task would have been simpler. He, therefore, set about extracting, compiling, and organizing such knowledge. The collated patent database and subsequent analysis revealed a natural pattern of innovation that can help solve similar technological problems. This study was continued, by Altshuller and his disciples, over the past 50 years and has yielded a systematic approach to definition and identification of innovative problems, a set of problem solving tools, and a vast knowledge database, which can help solve current technical problems in an innovative way. Today, the TRIZ software database includes the essence of over 2,500,000 patents. He defined 39 basic properties and 40 principles for solving problems containing contradiction in any two-of-39 properties. This he gave in the form of a contradiction table of size 39 x 39 with each cell giving up to 4 principles (and examples from patent data base), that may be used to eliminate the contradiction. Altshuller also laid the foundation for development of an analytical approach to solving inventive problems with an axiom – "The evolution of all technical systems is governed by objective laws". Improvement of any part of a system which has already reached the highest level of functional performance will lead to conflict with another part. This will lead to eventual improvement of the less evolved part(s). Such a continuing and self-sustaining process will bring the system closer to its ‘ideal’ state. Su-Field analysis ( "two Su bstances and one Field ") is used whenever a new function is introduced or modified (either inadvertently or intentionally) and inventive "standard solutions" (and examples from patent database) are available to find an analogous solution. ARIZ – ‘ Algorithm for Inventive Problem Solving’is used when systems mature and become complex thus making it difficult to modify or improve them in an incremental fashion. Anticipatory Failure Determination and Directed Evolution are some of the more recent additions (1992-) to the tools of TRIZ. Only a brief introduction is included.
  • Silicon Beach Training The focus of Six Sigma is fundamentally about quality, customer focus and cost, where as Lean is about cost and speed. Brighton, UK
  • Statistics and experimental design

    1. 1. Statistics and Experimental Design Shirley Coleman Industrial Statistics Research Unit ISRU
    2. 2. Outline of Talk <ul><li>Purpose of Stats and Experimental Design </li></ul><ul><li>History and Applications </li></ul><ul><li>Skill set needed </li></ul><ul><li>Examples </li></ul><ul><ul><li>Importance of planning </li></ul></ul><ul><ul><li>Subtleties </li></ul></ul><ul><li>Summary </li></ul>
    3. 3. Purpose of Statistics and Experimental Design <ul><li>Investigate </li></ul><ul><li>Make objective decisions </li></ul><ul><li>Experiment efficiently </li></ul><ul><li>Ensure reproducibility </li></ul><ul><li>Build a model </li></ul><ul><li>Predict </li></ul><ul><li>Monitor </li></ul><ul><li>………. </li></ul>
    4. 4. History of experimental design <ul><li>Agriculture </li></ul><ul><li> </li></ul><ul><li>Oldest agricultural research station </li></ul><ul><li>Rothamsted, Park Grass, 1856 </li></ul><ul><li>Cockle Park, Palace Leas, 1897 </li></ul>
    5. 5. Long term grass experiments Palace Leas, Cockle Park, Northumberland 1897 Park Grass, Rothamsted Herts, 1856
    6. 6. Palace Leas, Cockle Park
    7. 7. Palace Leas <ul><li>Experiment on effect of fertilisers on hay yield </li></ul><ul><ul><li>Can also look at root structure, species,… </li></ul></ul><ul><li>Meteorological station in next field from 1898 </li></ul><ul><li>14 plots of land </li></ul><ul><ul><li>8 for an experiment with N,P and K </li></ul></ul><ul><ul><li>6 additional (some abandoned in WWII) </li></ul></ul><ul><li>Results were apparent in1898 </li></ul><ul><li>Fabulous set of data </li></ul>
    8. 8. Palace Leas plots
    9. 9. Palace Leas plots
    10. 10. Rothampsted, Park Grass
    11. 12. Importance of publishing! COLEMAN, S.Y., SHIEL, R.S & EVANS, D.A. (1987) The effect of weather and nutrition on the yield of hay from Palace Leas meadow hay plots, at Cockle Park Experimental Farm, over the period from 1897 to 1980. Grass and Forage Science 42, 353-358.
    12. 16. History and Applications <ul><li>Agriculture </li></ul><ul><li>Given industrial slant by G.Taguchi </li></ul><ul><li>(b 1924, published 1951, in NE 2000) </li></ul><ul><li>Used in manufacturing </li></ul><ul><li>Gradually used in </li></ul><ul><ul><li>Business, service, health, </li></ul></ul><ul><ul><li>Finance, marketing, </li></ul></ul><ul><li>Bespoke nomenclature </li></ul>
    13. 17. Skill set needed <ul><li>Logical thinking </li></ul><ul><li>Attention to detail </li></ul><ul><li>Presentation skills </li></ul><ul><li>Analytical tools </li></ul><ul><li>Knowledge of where to go next </li></ul><ul><ul><li>Optimisation, RSA, simulation…… </li></ul></ul>
    14. 18. Examples <ul><li>Pressure, temperature, pointer setting, </li></ul><ul><ul><li>haul off speed, welding current, </li></ul></ul><ul><ul><li>granule size, nozzle width,…. </li></ul></ul><ul><li>N, P, K </li></ul><ul><li>Beer experiment </li></ul>
    15. 19. <ul><li>Beer experiment </li></ul><ul><li>(What affects frothing when pouring beer?) </li></ul>
    16. 21. Management Methodology <ul><li>Six Sigma </li></ul><ul><ul><li>D efine </li></ul></ul><ul><ul><li>M easure </li></ul></ul><ul><ul><li>A nalyse </li></ul></ul><ul><ul><li>I mprove </li></ul></ul><ul><ul><li>C ontrol </li></ul></ul><ul><li>Lean </li></ul><ul><li>PDCA </li></ul>
    17. 22. Lean Six Sigma <ul><li>Lean focuses on removing complexity </li></ul><ul><li>Six Sigma focuses on process improvement </li></ul><ul><li>Lean Six Sigma attempts to combine the best of both </li></ul><ul><li>Lean involves less statistics and is very popular in </li></ul><ul><li>some applications, such as healthcare. </li></ul>
    18. 23. <ul><li>Define problem </li></ul><ul><ul><li>QI tools, brain-storming, team roles </li></ul></ul><ul><ul><li>Identifying factors and levels </li></ul></ul><ul><li>Measurement issues </li></ul><ul><ul><li>Decide what, how, when, who and where to measure </li></ul></ul><ul><li>Analyse </li></ul><ul><ul><li>Use current knowledge, </li></ul></ul><ul><ul><li>Set experimental design and pilot </li></ul></ul><ul><li>Improve </li></ul><ul><ul><li>Run experiment and analyse </li></ul></ul><ul><li>Control </li></ul><ul><ul><li>Recommend method for best or least froth </li></ul></ul><ul><ul><li>Look for other opportunities to use what has been learnt </li></ul></ul>
    19. 24. Team roles <ul><li>Secretary </li></ul><ul><li>Waiter </li></ul><ul><li>Pourer </li></ul><ul><li>Measurer </li></ul><ul><li>Observers </li></ul>
    20. 25. Factors <ul><li>Materials ( beer type , temperature of bottles) </li></ul><ul><li>Machines ( glass shape ) </li></ul><ul><li>Man (steadiness) </li></ul><ul><li>Milieu (pressure, humidity, temperature) </li></ul><ul><li>Method ( angle , speed, height, time opened) </li></ul><ul><li>Measures (volume, height) </li></ul>
    21. 26. Experimental design <ul><li>More information out requires more data in </li></ul><ul><li>However, statistically designed experiments </li></ul><ul><li>help reduce the number of trials with least </li></ul><ul><li>reduction in information </li></ul><ul><li>Eg up to 7 factors can be tested in 8 trials </li></ul><ul><li>Taguchi uses Plackett-Burman designs </li></ul><ul><li>Eg up to 11 factors can be tested in 12 trials </li></ul>
    22. 27. Saturated L 8 design 1 1 1 1 1 1 1 8 -1 1 -1 1 -1 1 -1 7 -1 -1 1 1 -1 -1 1 6 1 -1 -1 1 1 -1 -1 5 -1 -1 -1 -1 1 1 1 4 1 -1 1 -1 -1 1 -1 3 1 1 -1 -1 -1 -1 1 2 -1 1 1 -1 1 -1 -1 1 G F E D C B A Trial
    23. 28. Taguchi saturated L 8 design 2 1 1 2 1 2 2 8 1 2 2 1 1 2 2 7 1 2 1 2 2 1 2 6 2 1 2 1 2 1 2 5 1 1 2 2 2 2 1 4 2 2 1 1 2 2 1 3 2 2 2 2 1 1 1 2 1 1 1 1 1 1 1 1 G F E D C B A Trial
    24. 29. Identifying factors and levels <ul><li>3 factors each at 2 levels </li></ul><ul><li>Factors - + </li></ul><ul><li>Beer type Belgian French </li></ul><ul><li>Glass type Flat Rounded </li></ul><ul><li>Glass angle Upright Tilted </li></ul><ul><li>Response Froth height (mm) </li></ul>
    25. 30. Orthogonal array 1 1 1 8 1 1 -1 7 1 -1 1 6 1 -1 -1 5 -1 1 1 4 -1 1 -1 3 -1 -1 1 2 -1 -1 -1 1 Angle Glass Beer Trial
    26. 31. Experimental trials <ul><li>Eg Belgian beer poured into a flat </li></ul><ul><li>bottomed glass without tilting </li></ul><ul><li>Eg French beer poured into a round </li></ul><ul><li>bottomed glass without tilting </li></ul>
    27. 32. Randomisation <ul><li>Reduces false replication and bias </li></ul><ul><li>Eg drug trial </li></ul><ul><ul><li>first group of mice have treatment and </li></ul></ul><ul><ul><li>second have placebo, </li></ul></ul><ul><li>if mice are selected by grabbing from cage, </li></ul><ul><li>fittest are caught last and placebo can </li></ul><ul><li>appear to be better than the treatment </li></ul>
    28. 33. Team roles <ul><li>Secretary : Read trial and register result </li></ul><ul><li>Waiter : Pick the right glass and bottle </li></ul><ul><li>Pourer : Pour the beer into the glass </li></ul><ul><li>Measurer : Use the ruler to read off the froth </li></ul><ul><li>Observers: Note that procedures are followed </li></ul>
    29. 34. Main effects plot
    30. 35. Factors and factor levels <ul><li>Factors - + </li></ul><ul><li>Beer type Belgian French </li></ul><ul><li>Glass type Flat Rounded </li></ul><ul><li>Glass angle Upright Tilted </li></ul><ul><li>Response Froth height (mm) </li></ul>
    31. 36. Interaction plot: glass*angle
    32. 37. ANOVA table for beer       3468 15 Total     29 260 9 Error 0.56 0.37 11 11 1 Beer*Glass 0.96 0 0 0 1 Beer*Angle 0.00 22.06 638 638 1 Glass*Angle 0.00 77.26 2233 2233 1 Angle 0.03 6.54 189 189 1 Glass 0.06 4.78 138 138 1 Beer P F MS SS DF Source
    33. 38. Graphical analysis of significance
    34. 40. Context and implications <ul><li>Know which glasses to buy </li></ul><ul><li>Know how to pour </li></ul><ul><li>Adapt to alternative requirements, eg no froth </li></ul><ul><li>Apply methodology in other contexts </li></ul>
    35. 41. Other examples <ul><li>Human Resources </li></ul><ul><ul><li>Training requirements </li></ul></ul><ul><ul><li>Explore effects of commands given </li></ul></ul><ul><li>Accounts </li></ul><ul><ul><li>Explore effect of timing and nature </li></ul></ul><ul><ul><li>of reminders </li></ul></ul><ul><li>Preferences </li></ul><ul><ul><li>Explore trade-offs </li></ul></ul><ul><ul><li>Conjoint analysis </li></ul></ul>
    36. 42. Conjoint Analysis <ul><li>Customers CONsider JOINTly and give their opinions, </li></ul><ul><li>trading off factors to reach a desired end. </li></ul><ul><li>For example, to design a conference, consider: </li></ul><ul><ul><li>In University or hotel </li></ul></ul><ul><ul><li>2 days or 3 days </li></ul></ul><ul><ul><li>Evening speaker or not </li></ul></ul><ul><ul><li>20 minute or longer talks </li></ul></ul><ul><ul><li>… . </li></ul></ul><ul><li>Present the different options, eg in a questionnaire and analyse results </li></ul><ul><li>Helps determine what people value in different product features </li></ul><ul><li>or service attributes. </li></ul>
    37. 43. Format of questions (ENBIS) <ul><li>‘ How successful do you think the following </li></ul><ul><li>conference would be?’ </li></ul><ul><li>An informal, applied conference held in a </li></ul><ul><li>conference suite that has an evening session, </li></ul><ul><li>it mostly features presentations involving </li></ul><ul><li>industrialists’ </li></ul><ul><li>1= not very successful 5= very successful </li></ul>
    38. 44. Results - ENBIS <ul><li>ANOVA with categorical responses gave </li></ul><ul><li>Applied vs theoretical and </li></ul><ul><li>Industrialists vs academics </li></ul><ul><li>as important factors </li></ul>
    39. 45. Results - ENBIS <ul><li>Taguchi style analysis for the variability of </li></ul><ul><li>responses showed </li></ul><ul><li>significantly greater variation in views about </li></ul><ul><li>applied talks than for theoretical talks </li></ul><ul><li>significantly greater variation for </li></ul><ul><li>workshops than for presentations </li></ul>
    40. 46. Online Conjoint Analysis <ul><li>Used in automobile feature testing to find the features </li></ul><ul><li>consumers are willing to give up in order to get something </li></ul><ul><li>they value more. </li></ul><ul><li>Outcomes help guide new product design, old product </li></ul><ul><li>redesign or repositioning decisions. </li></ul><ul><li>Used in travel industry to determine how much consumers </li></ul><ul><li>are willing to pay for a ticket in order to get more leg room. </li></ul>Building “Voice of Customer” into Product Development Source: Siegel (2004)
    41. 47. Other examples <ul><li>Kansei Engineering </li></ul><ul><li>Incorporates emotion into design </li></ul><ul><ul><li>Orthogonal array for products </li></ul></ul><ul><ul><li>Semantic scales for emotion </li></ul></ul><ul><ul><li>Sample of customers </li></ul></ul><ul><li>Highly developed in Japan </li></ul><ul><li>KENSYS 2003-6 in Europe </li></ul>
    42. 49. Analysis relates emotions to design <ul><li>Model </li></ul><ul><ul><li>Response is happiness </li></ul></ul><ul><ul><li>Design factors are colour, style, heel, etc </li></ul></ul><ul><li>Aim is to advise designers </li></ul><ul><ul><li>Which shoes will give the desired emotional </li></ul></ul><ul><ul><li>response </li></ul></ul><ul><ul><li>How to develop a balanced portfolio </li></ul></ul><ul><li>Similar results for logistic regression or ANOVA </li></ul>
    43. 50. Design a waiting room <ul><li>Design factors </li></ul><ul><ul><li>Sofa or chair </li></ul></ul><ul><ul><li>Lighting soft or bright </li></ul></ul><ul><ul><li>Service desk </li></ul></ul><ul><ul><li>Windows </li></ul></ul><ul><li>Other factors </li></ul><ul><ul><li>Waiting time max 30 minutes </li></ul></ul><ul><ul><li>…… .. </li></ul></ul>
    44. 51. <ul><li>Please rate where you feel </li></ul><ul><li>the image fits on each of the </li></ul><ul><li>following semantic scales. </li></ul>Comfortable Uncomfortable At Ease Uneasy Efficient Inefficient Trustworthy Untrustworthy Calm Stimulating Boring Interesting 1 2 3 4 5
    45. 52. Design Rules Comfortable Seating (sofa) Windows (yes) Lighting (soft) Service desk (yes) Seating (chair) Service desk (yes) Max Waiting Time (30min) Efficient
    46. 53. Key Drivers of Satisfaction <ul><li>[Ease of Use] [ Navigation, clarity, fresh/relevant content, etc. ] </li></ul><ul><li>[Graphic Style] [ Colour, layout, print size, type, no. of photographs, </li></ul><ul><li>graphics and animation . ] </li></ul><ul><li>[ Perceived channel advantage ] [ Price, Speed, etc . ] </li></ul><ul><li>[ Privacy and Security ] [ Brand, reputation, appearance of the site (more </li></ul><ul><li>imp than security logos appearing on website) ] </li></ul><ul><li>[ Fulfilment and Reliability ] [ Timeliness of service, availability, breadth and depth of </li></ul><ul><li>products/services, responsiveness/access (availability of service </li></ul><ul><li>personnel, multiple communication channels) and personalisation. ] </li></ul>Source: Baur, Schmidt & Hammersmith, 2006
    47. 54. Website design process The Brief Trial Pages The Prototype The Prototype Client requirements and goals Launch Approval Response and refinement CLIENT WEB DESIGN FIRM Strategic planning, engineering Style book, training, quality tests Final design, testing and coding Design content and marketing User Survey Conjoint Analysis Kansei Design for Emotional Appeal Content & Navigation SPC Building “Voice of Customer” into Design by courtesy of A.Parulekar Web Design for Sticky Relationship
    48. 55. Statistics <ul><li>Quantitative management </li></ul><ul><ul><li>Software </li></ul></ul><ul><ul><li>Graphical </li></ul></ul><ul><ul><li>Tabular </li></ul></ul><ul><li>Comparative tests, ANOVA </li></ul><ul><li>Statistical models </li></ul><ul><ul><li>Regression </li></ul></ul><ul><ul><li>Logistic regression </li></ul></ul><ul><li>Multivariate analysis </li></ul>
    49. 56. Tutorials, eg MINITAB <ul><li>These easy step-by-step tutorials introduce you to the </li></ul><ul><li>Minitab environment and provide a quick overview of </li></ul><ul><li>some of Minitab's most important features. The tutorials </li></ul><ul><li>are designed to explain the fundamentals of using Minitab: </li></ul><ul><li>how to use the menus and dialog boxes, how to manage </li></ul><ul><li>and manipulate data and files, how to produce graphs, …. </li></ul><ul><li>Session One: Graphing Data </li></ul><ul><li>Session Two: Entering and Exploring Data </li></ul><ul><li>Session Three: Analyzing Data </li></ul><ul><li>Session Four: Assessing Quality </li></ul><ul><li>Session Five: Designing an Experiment </li></ul>
    50. 57. Data exploration, eg SAS JMP Key processes and inputs associated with excessive variation in 60-minute dissolution Recursive Partitioning Decision Tree
    51. 58. Importance of planning <ul><li>Collecting all the data that is needed </li></ul><ul><li>Getting the right people involved </li></ul><ul><li>Getting the right materials in place </li></ul><ul><li>Ensuring time for input from others </li></ul><ul><li>Poke yoka </li></ul>
    52. 59. Subtleties include <ul><li>Measurement issues </li></ul><ul><li>Sample sizes </li></ul><ul><ul><li>Use continuous variables where possible </li></ul></ul><ul><ul><li>Robustness </li></ul></ul><ul><li>Bias and confounding, especially time trends </li></ul><ul><li>Piloting </li></ul>
    53. 60. Summary <ul><li>All of the above </li></ul><ul><li>Thanks </li></ul>