DESIGNING COMPUTER EXPERIMENTS TO DETERMINE ROBUST CONTROL VARIABLES
Jeffrey S. Lehman, J. Santner, William I. Notz · 2004
This paper is concerned with the design of computer experiments when there are two types of inputs: control variables and environmental variables. Con- trol 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 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 re- sponse 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 stochas- tic process. Given the previous information, the sequential algorithm computes for each untested site the over the current guess of the optimal robust setting. The design selects the next site to maximize the expected improvement