This talk will describe the sequential design of a computer experiment to choose robust sets of control input variables when there are two types of inputs: control variables and environmental variables. Control (``engineering'') design variables are determined by a product designer while environmental (``noise'' or ``field'') variables are determined by field conditions but take values that are assumed to be characterized by a probability distribution. Roughly, 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. This talk presents a sequential strategy to select the inputs at which to observe the response and a corresponding strategy to determine a robust setting of the control variables. The solution we suggest for this problem is Bayesian; the prior for the output function is a stationary Gaussian stochastic process. Given the previous information, the sequential algorithm computes, for each untested input, the ``improvement'' over the current guess of the optimal robust setting. The design selects the next site to maximize the expected improvement criterion.
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