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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. Outline. Introduction Evaluation over a Fixed Set of Points Evaluation over a Random Set of Points Conclusions. Introduction.
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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
Outline • Introduction • Evaluation over a Fixed Set of Points • Evaluation over a Random Set of Points • Conclusions
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.
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
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
Evaluation over a Fixed Set of Points • The average prediction variance: The second method The first method p/N
Evaluation over a Fixed Set of Points • IV-criterion:
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.
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.