A Comparison of Prediction Variance Criteria for Response Surface Designs

1. A Comparison of Prediction Variance Criteria for Response Surface Designs 指導教授：童超塵 作者：JOHNJ.BORKOWSKI 主講人：廖莉芳

2. Outline • Introduction • Evaluation over a Fixed Set of Points • Evaluation over a Random Set of Points • Conclusions

3. Introduction • A response surface design is implemented that will enable the experimenter to fit the second-order model given by • An N-point response surface design can be represented by an N × k design matrix.

4. Introduction • Four different types of composite designs will be studied for3,4,and5designfactors: • The central composite designs (CCDs)k=3、4、5 • The Plackett–Burman composite designs (PBCDs)k=4、5 • The small composite designs (SCDs)k=3、4 • The Notz designsk=3、4、5

5. Evaluation over a Fixed Set of Points • The average prediction variance (APV)where • IV-criterion: • Take the average of x’(X’X)-1x over the points in the design. • The first method: • Use N-point design, the average leverage for a p-parameter polynomial model is p/N. • The second method: • The average of x’(X’X)-1x

6. Evaluation over a Fixed Set of Points • The average prediction variance: The second method The first method p/N

7. Evaluation over a Fixed Set of Points • IV-criterion:

8. Evaluation over a Fixed Set of Points • This method will yield larger values and highlights the slow convergence to the exact IV-value as the size of the evaluation set increases.

9. Evaluation over a Random Set of Points

10. Conclusions • If the estimate of IV is the average taken over a relatively large random set of evaluation points, it will be reliable. • Recommend: • Planning to use IV as a design evaluation criterion determine the exact value and, in general, not use the APV values provided by statistical software packages as estimates.