Correlated simulation experiments

Abstract

This paper studies the effects of using correlated random-number streams in replications of a simula tion experiment in which output is to be related to input by linear or quadratic response surfaces. For the linear case, it is shown that either positively or negatively correlated streams produce a smaller generalized variance for the least-squares estimates than occur when the streams are independent. Al though the prediction variance is small with nega tively correlated streams, positively correlated streams produce a smaller variance for the estimated slope. In the quadratic case it is shown that of twenty- seven possible input correlation designs only six guarantee a smaller generalized variance. Only one of these produces a smaller prediction variance. However, no plan will guarantee a smaller slope variance. In the quadratic case one often wants the slope variance to be as small as possible since the objective of the study may be to determine where the maximum or minimum response occurs in terms of the input.