Systems Management Control Concepts

1. Systems ManagementControl Concepts “It is the mark of a truly intelligent person to be moved by statistics.” George Bernard Shaw

2. R. A. Fisher • Studied math and astronomy at Cambridge • Conducted agricultural research in Britain • Developed powerful methods of experimental design Sir Ronald A. Fisher 1890 - 1962

3. Lady Tasting Tea • At a summer tea party in Cambridge, England, a lady states that tea poured into milk has a different taste than milk poured into tea • Most guests, including distinguished scientists, think this nonsense, but Ronald Fisher proposes a method to scientifically test the lady's claim • In Fisher’s experiment, the lady correctly identified every cup! Salsburg, D., The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century,” W.H. Freeman, 2001

4. A Cure for Scurvy • Scurvy once common among sailors • Dr. James Lind, a Scottish surgeon in the British Royal Navy, designed experiments in 1754 • 12 scurvy patients on the HMS Salisbury selected • Divided into six pairs and given remedies • Cider, vitriol, seawater, garlic, vinegar, citrus • The pair on oranges and lemons fit for duty in six days • First controlled clinical trial • Origin of “limey” as term for British sailors Lind, J. , A Treatise of the Scurvy, 1753

5. Design of Experiments • As we vary process parameters to reduce the loss function, it may be hard to determine what changes cause what effects • Traditional method is to vary one parameter at a time • Inefficient • Provides no information about interactions

6. Example • Goal: improve some quality characteristic • Factors: temperature (T) and pressure (P) • Approach: conduct a series of experiments • First, the classic one factor at a time design • Baseline plus 2 trials

7. One Factor at a Time Design • The “T-effect”  increase result by 10 • The “P-effect”  increase result by 20 • Each estimate based on two trials • No estimate of the interaction effect

8. Factorial Design • The T-effect (20+26)/2 – (10+30)/2 = 3 • The P-effect (30+26)/2 – (20+10)/2 = 13 • Each estimate based on four trials • Next, interaction effect

9. Factorial DesignTxP Interaction Effect • T-effect (P Low) 20 – 10 = 10 • T-effect (P High) 26 – 30 = -4 • By convention TxP effect is half the difference (10+4) / 2 = 7 • Average of two T-effects equal to main effect of T [10 + (-4)] / 2 = 3

10. Factorial DesignInteraction Effect Best result Interaction: Effect of T changes depending on level of P

11. Factorial DesignPxT Interaction Effect • P-effect (T Low) 30 – 10 = 20 • P-effect (T High) 26 – 20 = 6 • Half the difference is the PxT effect (same as TxP) (20-6) / 2 = 7 • Average of two P-effects equal to main effect of P [20 + 6] / 2 = 13

12. Factorial DesignLurking Variable • Suppose Operator also affects the response • T and O perfectly correlated • Which variable caused the effect attributed to T? • Control what you can • Randomize trial order to break link with variables you can’t control (or don’t know about)

13. Factorial DesignSummary • With only four trials, we get • Main effect of T • Main effect of P • 2-factor interaction effect • Each estimate based on all four trails • Estimating effects  ANalysis Of Means (ANOM) • Determining which effects are statistically significant  ANalysis Of VAriances (ANOVA) With good design, analysis can be simple

14. Factorial Design • Same as earlier example • Here with algebraic notation • Recall that T-effect = 3 P-effect = 13 T x P effect = 7 • Much easier to get these results with this notation

15. Calculating Effects in the 23 Design

16. The Fractional Factorial • One-half fraction of a full 23 design: 23-1 design • Note that effects B, AB and BC, ABC are confounded • We always lose something with a fractional design

17. Fractional Factorial Designs • As the number of factors increases, the runs required for a full factorial may outgrow the experimental resources available • Fractional factorial designs are used for screening experiments: to determine which factors are truly significant • Goal: distinguish main effects and 2-factor interactions

18. Alias structure for 26-2 design

19. Design Resolution • Resolution III Designs (23-1) • No main effects are aliased with any other main effect, but main effects are aliased with 2-factor interactions • Resolution IV Designs (24-1) • No main effect is aliased with any other main effect or 2-factor interaction, but 2-factor interactions are aliased with each other • Resolution V Designs (25-1) • No main effect or 2-factor interaction is aliased with any other main effect or 2-factor interaction

20. George Box • Born in Britain • Distinguished career at the University of Wisconsin • Box, Hunter, and Hunter, Statistics for Experimenters • Dr. John MacGregor one of Box’s Ph.D. students George E. P. Box 1919 -

21. Douglas Montgomery • Ph.D. VPI, 1969 • G.T. faculty, 1969 - 84 • ASU faculty, 1988 – present • ACQC Shewhart Medal, 1997 • Supervised Philip Coyle’s M.S. thesis, "An Adaptation of Bayesian Statistical Methods to the Determination of Optimal Sample Sizes for Operational Testing"

22. How to use statistical techniques • Find out as much as you can about the problem • Get help from experts on the process • Define objectives • Don’t invest more than one quarter of the experimental effort (budget) in a first design • Box, G., Hunter, W., Hunter, S., Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, John Wiley and Sons, 1978

23. How to use statistical techniques • Use your non-statistical knowledge of the problem • Keep the design and analysis as simple as possible • Recognize the difference between practical and statistical significance • Experiments are usually iterative • Montgomery, D., Design and Analysis of Experiments, 2nd edition, John Wiley and Sons, 1984