On cascading latin hypercube designs and additive models for experiments

This paper is concerned with aspects of the design and analysis of computer experiments. It has been motivated by issues in the experimental design of integrated-circuits. Suppose we wish to model the behavior of a complex process as a function of several factors. An appealing approach is to model the response of the system as a stochastic process (Sacks, Welch, Mitchell and Wynn (1989)). Often much of the variation in the response can be accounted for by an additive function in each of the factors. In this paper we consider a promising additive stochastic model proposed by Stein (1989). We introduce Cascading Latin hypercube designs as an efficient basis for statistical inference on the stochastic structure when the number of initial inputs is large. Comparisons are made to simple random designs, Faure (1982) designs and ordinary Latin hypercube designs. The results provide insight into the optimal design under such models. © 1991 by Marcel Dekker, Inc