1. Examples of Designed Experiments With Nonnormal Responses
SHARON L. LEWIS, DOUGLAS C. MONTGOMERY and
RAYMOND H. MYERS
Journal of Quality Technology, 33, pp , 2001
演講者: 張秉鈞

2. Outline Introduction Example 1: The Drill Experiment
Example 2: The Windshield Molding Slugging Experiment
Conclusion

3. Introduction In general, linear model :
Check model’s three basic assumption
1. Normal probability plot
2. Residuals plot
Nonnormal responses
1. data transformations
2. GLM (Generalized Linear Models)

4. Generalized Linear Models
Three components:
(1) Response distribution is exponential family
(Binomial, Poisson, Gamma, Normal, etc)
(2) Linear predictor
(3) Link function
(relationship between the and )

5. More details: Introduction to Linear Regression Analysis
(Chapter 13)
Software packages: SAS, S-PLUS
Objective: To compare two approaches by designed
experiments with nonnormal responses
Criterion: Lengths of confidence intervals of mean response

6. The Drill Experiment unreplicated factorial design advance rate
drill load
flow rate
rotational speed
type of drilling mud used
GLM: Gamma distribution, log link function

7. Effect Estimates

8. Half -Normal Probability Plot
, and are significant effects
data transformation model:
GLM model:

9. 95% Confidence Interval On the Means

10. The Windshield Molding Slugging Experiment
During the stamping process, debris carried into the die appears as slugs in the product
fractional factorial design, and resolution III
number of good parts out of 1000
poly-film thickness (0.0025, )
oil mixture (1:20, 1:10)
gloves (cotton, nylon)
metal blanks (dry underside, oily underside)

11. Design Matrix and Response Data
data transformation: logistic
GLM: Binomial distribution, logistic link function

12. Hamada and Nelder (1997) Effect Estimates Std. Err. t Intercept -0.513
0.28
-1.80
2.971
0.46
6.43
-0.270
0.32
-0.84
1.329
2.88
0.351
0.76

13. Refit the Model (GLM)
We fit the model with factors

14. 95% Confidence Intervals On the Means

17. Conclusion
Data transformations may be inappropriate for some situations
With the GLM, normality and constant variance are not required
With the GLM, length of confidence interval is short

18. References
HAMADA, M. and NELDER, J. A. (1997). “Generalized Linear Models for Quality-Improvement Experiments”. Journal of Quality Technology 29, pp
MONTGOMERY, D. C. (2001). Design and Analysis of Experiments, 5th ed. John Wiley & Sons, Inc., New York, NY
MONTGOMERY, D. C. and PECK, E. A. (1992). Introduction to Linear Regression Analysis, 2th ed. John Wiley & Sons, Inc., New York, NY
MYERS, R. H. and MONTGOMERY, D. C. (1997). “A Tutorial on Generalized Linear Models”. Journal of Quality Technology 29, pp