A General Approach to Multiple Response Surface Optimization
Based upon Posterior Predictive Distributions
John J. Peterson
GlaxoSmithKline Pharmaceuticals
Phone: (610) 270-5303
FAX: (610) 270-5480
709 Swedeland Road
Mail code: UW281A
King of Prussia, PA 19406-0939
Guillermo Miro-Quesada
Dept. of Industrial & Manufacturing Engineering
310 Leonhard building
Penn State University
University Park, PA 16802
Enrique del Castillo
Dept. of Industrial & Manufacturing Engineering
Ph: (814) 863 6408
310 Leonhard building
Penn State University
University Park, PA 16802
Presenter: John J. Peterson
Key words: posterior predictive distribution, noise variables, robust parameter optimization,
split-plot experiment, seemingly unrelated regression model.
Purpose: To present a general methodology for multiple response surface optimization that also
provides the experimenter with a measure of the reliability of the conformance of their
optimization to specifications.
Abstract:
This paper presents a general approach to multiple response surface optimization that not only
provides optimal operating conditions, but also measures the reliability of an acceptable quality
result for any set of operating conditions. The most utilized multiple response optimization
approaches of "overlapping mean responses" or the desirability function do not do not take into
account the variance-covariance structure of the data nor the model parameter uncertainty.
Some of the quadratic loss function approaches take into account the variance-covariance
structure of the predicted means, but they do not take into account the model parameter
uncertainty associated with variance-covariance matrix of the error terms. For the optimal
conditions obtained by these approaches, the probability that they provide a good multivariate
response, as measured by that optimization criterion, can be unacceptably low. Furthermore, it is
shown that ignoring the model parameter uncertainty can lead to reliability estimates that are far
too large. The proposed approach can be used with any of the current multiresponse
optimization procedures to assess the reliability of a good future response. This approach takes
into account the correlation structure of the data, the variability of the process distribution, and
the model parameter uncertainty. This method is easily extended to handle the presence of noise
variables. Using Markov Chain Monte Carlo methods, this approach can also be extended to
seemingly unrelated regression models and split-plot experiments. This utility of this method is
illustrated with some examples.
Session Preference: Statistics
Where did you learn about the Call for Papers? : At the 2002 FTC