1. Diploma in Statistics Design and Analysis of Experiments Lecture 1.11 Diploma in Statistics Design and Analysis of Experiments Lecturer:Dr. Michael Stuart, Department of Statistics Office:LB 101 email:Michael.Stuart@tcd.ie Too short; cover parts 1-3 in first half; need more for the 2nd half. Try boys shoes, comparing two t-tests

2. Diploma in Statistics Design and Analysis of Experiments Lecture 1.12 Design and Analysis of Experiments Course Outline Experimental and observational studies Basic design principles for experiments –Randomisation –Blocking (pairing) –Factorial structure Standard designs, illustrated

3. Diploma in Statistics Design and Analysis of Experiments Lecture 1.13 Design and Analysis of Experiments Course Outline Analysis of experimental data –Exploratory data analysis –Parameter estimation and significance testing –Analysis of variance –Model validation, diagnostics Computer laboratories Strategies for Experimenting

4. Diploma in Statistics Design and Analysis of Experiments Lecture 1.14 Design and Analysis of Experiments References Mullins, E., Statistics for the Quality Control Chemistry Laboratory, Royal Society of Chemistry, 2003, particularly Chapters 4-5, 7-8. Detailed coverage of much of the module, in a specific context. Montgomery, D.C., Design and analysis of experiments, 6th ed., Wiley, 2005. A comprehensive text, covers much more than this module, including statistical theory. Not always authoritative.

5. Diploma in Statistics Design and Analysis of Experiments Lecture 1.15 Design and Analysis of Experiments Further reading Box, G.E.P, Hunter, J.S. and Hunter, W.G., Statistics for Experimenters, 2nd. ed., Wiley, 2005. Includes many gems of wisdom from these masters of the genre, though not a course text. Daniel, C., Applications of Statistics to Industrial Experimentation, Wiley, 1976. Includes many gems of wisdom from this master of the genre, using methodology appropriate for an industrial setting. Altman, D.G., Practical Statistics for Medical Research, Chapman & Hall / CRC, 1991. Does what it says on the tin!

6. Diploma in Statistics Design and Analysis of Experiments Lecture 1.16 Lecture 1.1 1.Introduction to Course 2.Case study on process improvement statistical assessment of a process change strategy for experimentation 3.Experimental vs observational study another illustration 4.Multifactor designs efficiency interaction

7. Diploma in Statistics Design and Analysis of Experiments Lecture 1.17 2 Case study on process improvement Comparison of standard (old) and new processes for manufacture of electronic components Key issues –homogeneity for valid comparison –systematic allocation –random allocation

8. Diploma in Statistics Design and Analysis of Experiments Lecture 1.18 Experimental design 50 components sampled per day, 6 days per week, 8 weeks, Systematic layout, as follows

9. Diploma in Statistics Design and Analysis of Experiments Lecture 1.19 Results Numbers of defectives per daily sample of 50 for 48 days (8 weeks)

10. Diploma in Statistics Design and Analysis of Experiments Lecture 1.110 Comparison of two processes over eight weeks: data for first four weeks

11. Diploma in Statistics Design and Analysis of Experiments Lecture 1.111 Comparison of two processes over eight weeks: data for last four weeks, with eight week summary

12. Diploma in Statistics Design and Analysis of Experiments Lecture 1.112 Differences in numbers defective, with control limits No statistical significance!

13. Diploma in Statistics Design and Analysis of Experiments Lecture 1.113 Alternative design (proposed by engineers) Assume this design was used; check for no effect

14. Diploma in Statistics Design and Analysis of Experiments Lecture 1.114 Defect rates, per cent, with differences, for the first and second four week periods

15. Diploma in Statistics Design and Analysis of Experiments Lecture 1.115 Defect rates, per cent, with differences, for the first and second four week periods highly statistically significant!

16. Diploma in Statistics Design and Analysis of Experiments Lecture 1.116 Exercise Assess the statistical significance of the difference in defect rates, %, between the first period and second period for the old process. Homework Assess the statistical significance of the difference in defect rates, %, between the first period and second period for the new process.

17. Diploma in Statistics Design and Analysis of Experiments Lecture 1.117 Numbers defective in time order Long term downward trend, systematic bias How can this be?

18. Diploma in Statistics Design and Analysis of Experiments Lecture 1.118 How to avoid systematic bias Make comparisons under homogeneous experimental conditions 1Systematic arrangement, as implemented: avoids known biases 2Random allocation: within each day pair, allocate old and new processes at random avoids known and unknown biases

19. Diploma in Statistics Design and Analysis of Experiments Lecture 1.119 Two design principles Blocking –identify homogeneous blocks of experimental units –assess effects of experimental change within homogeneous blocks –average effects across blocks Randomisation –allocate experimental conditions to units at random

20. Diploma in Statistics Design and Analysis of Experiments Lecture 1.120 Strategy for Experimentation The SIPOC Process Model Customers Process Suppliers Inputs Outputs S IPOC

21. Diploma in Statistics Design and Analysis of Experiments Lecture 1.121 Strategy for Experimentation Statistical Thinking Customer Process Supplier Inputs Outputs Process management and improvement Input measures Process measures Process changes Output measures Supplier performance Customer Feedback

22. Diploma in Statistics Design and Analysis of Experiments Lecture 1.122 Strategy for Experimentation Shewhart's PDCA Cycle

23. Diploma in Statistics Design and Analysis of Experiments Lecture 1.123 Strategy for Experimentation Shewhart's PDCA Cycle Plan:Plan a change to the process, predict its effect, plan to measure the effect Do:Implement the change as an experiment and measure the effect Check:Analyse the results to learn what effect the change had, if any Act:If successful, make the change permanent, proceed to plan the next improvement or if not, proceed to plan an alternative change

24. Diploma in Statistics Design and Analysis of Experiments Lecture 1.124 Strategy for Experimentation: new vs old manufacturing process Plan: Compare defect rates for old process and new (cheaper) process –predict reduction, or no increase, in number of defectives using new process Sample output over an eight week period, six days per week –select 50 components at random per day Count number of defectives per sample

25. Diploma in Statistics Design and Analysis of Experiments Lecture 1.125 Do: Implement plan Record daily numbers of defectives Assessing experimental process for manufacturing electronic components

26. Diploma in Statistics Design and Analysis of Experiments Lecture 1.126 Check: Analyse data test statistical significance of the change Assessing experimental process for manufacturing electronic components

27. Diploma in Statistics Design and Analysis of Experiments Lecture 1.127 Act: If no worse, make the change permanent, –proceed to plan the next improvement or if not, proceed to plan an alternative change Assessing experimental process for manufacturing electronic components

28. Diploma in Statistics Design and Analysis of Experiments Lecture 1.128 3 Observational vs Experimental study Alternative design: sample 1200 components from old process inventory, sample 1200 components from new process inventory, compare

29. Diploma in Statistics Design and Analysis of Experiments Lecture 1.129 Example 2: walking babies How long does it take a baby to walk? Can this be affected by special training programs? 4 "training" programs: 1. special exercises 2. normal daily exercise 3. weekly check 4. end of study check each of 24 babies allocated at random to groups of 6 in each program.

30. Diploma in Statistics Design and Analysis of Experiments Lecture 1.130 Example 2: walking babies

31. Diploma in Statistics Design and Analysis of Experiments Lecture 1.131 Example 2: walking babies Alternative design: each of 4 different consultants prescribes one of the four training programs, select a sample randomly from babies assigned to each program. Problems: assignment of babies to programs equivelent to assignment of mothers to consultants lurking variables!

32. Diploma in Statistics Design and Analysis of Experiments Lecture 1.132 Walking babies vs Defective components Level of control: less control means more variation

33. Diploma in Statistics Design and Analysis of Experiments Lecture 1.133 4 Multi-factor experiments Traditional versus statistical design –efficiency –interaction Several levels Several factors

34. Diploma in Statistics Design and Analysis of Experiments Lecture 1.134 Illustration of a traditional design, with 12 experimental runs Pressure Temperature High Low (best)

35. Diploma in Statistics Design and Analysis of Experiments Lecture 1.135 Illustration of a full factorial design, with 12 experimental runs Pressure Temperature High Low

36. Diploma in Statistics Design and Analysis of Experiments Lecture 1.136 Interaction between the factors Pressure Temperature High Low 65 75 70 60 5 15  5 5 5 best

37. Diploma in Statistics Design and Analysis of Experiments Lecture 1.137 Multilevel Interaction: Emotional Arousal 160 subjects, –80 male (M), –80 female (F) shown one of 4 pictures: –nude female, –nude male, –infant, –landscape. Response variable: –level of emotional arousal

38. Diploma in Statistics Design and Analysis of Experiments Lecture 1.138 Interaction between Factors Case study: Emotional Arousal

39. Diploma in Statistics Design and Analysis of Experiments Lecture 1.139 Non-linear response: Optimisation vs Improvement

40. Diploma in Statistics Design and Analysis of Experiments Lecture 1.140 Optimising performance; hill climbing

41. Diploma in Statistics Design and Analysis of Experiments Lecture 1.141 Optimising performance; hill climbing

42. Diploma in Statistics Design and Analysis of Experiments Lecture 1.142 Optimising performance; hill climbing

43. Diploma in Statistics Design and Analysis of Experiments Lecture 1.143 Optimising performance; hill climbing

44. Diploma in Statistics Design and Analysis of Experiments Lecture 1.144 Optimising performance; hill climbing

45. Diploma in Statistics Design and Analysis of Experiments Lecture 1.145 Several factors 2 - level factors:2 factors:2 2 = 4 runs 3 factors:2 3 = 8 runs 4 factors:2 4 = 16 runs 5 factors:2 5 = 32 runs 6 factors:2 6 = 64 runs 7 factors:2 7 = 128 runs Multi-level:2 × 3 × 4 × 5 = 120 runs

46. Diploma in Statistics Design and Analysis of Experiments Lecture 1.146 Reading SASections 1.9, 11.4 - 11.6 EMSections 4.3, 4.5.1, 5.2 DCMSection 2.5, 3.1 - 3.3