, Thomas J. Santner
and William I. NotzBattelle Memorial Institute and
The Ohio State University
Abstract: This paper is concerned with the design of computer experiments when there are two types of inputs: control variables and environmental variables. Control variables, also called manufacturing variables, are determined by a product designer while environmental variables, called noise variables in the quality control literature, are uncontrolled in the field but take values that are characterized by a probability distribution. Our goal is to find a set of control variables at which the response is insensitive to the value of the environmental variables, a ``robust'' choice of control variables. Such a choice ensures that the mean response is as insensitive as possible to perturbations of the nominal environmental variable distribution. We present a sequential strategy to select the inputs at which to observe the response so as to determine a robust setting of the control variables. Our solution is Bayesian; the prior takes the response as a draw from a stationary Gaussian stochastic process. Given the previous information, the sequential algorithm computes for each untested site the ``improvement'' over the current guess of the optimal robust setting. The design selects the next site to maximize the expected improvement criterion.
Key words and phrases: Computer experiments, expected improvement, noise variables, robust control variables, robust optimization, sequential design.