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
國立雲林科技大學 工業工程與管理所
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.
國立雲林科技大學 工業工程與管理所
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 designs
k=3、4、5
國立雲林科技大學 工業工程與管理所
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
國立雲林科技大學 工業工程與管理所
Evaluation over a Fixed Set of Points
• The average prediction variance:
The first method p/N
The second method
國立雲林科技大學 工業工程與管理所
Evaluation over a Fixed Set of Points
• IV-criterion:
國立雲林科技大學 工業工程與管理所
Evaluation over a Fixed Set of Points
• This method will
yield larger values
and highlights the
slow convergence
to the exact IVvalue as the size
of the evaluation
set increases.
國立雲林科技大學 工業工程與管理所
Evaluation over a Random Set of Points
國立雲林科技大學 工業工程與管理所
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.
國立雲林科技大學 工業工程與管理所