Stochastic kriging with qualitative factors

Abstract

Stochastic kriging (SK) has been studied as an effective metamodeling technique for approximating the mean response surface implied by a stochastic simulation. Until recently, it has only been applied to simulation experiments with continuous decision variables or factors. In this paper, we propose a new method called stochastic kriging with qualitative factors (SKQ) that extends stochastic kriging to a broader scope of applicability. SKQ is able to build metamodels for stochastic simulations that have both quantitative (continuous) and qualitative (categorical) factors. To make this extension, we introduce basic steps of constructing valid spatial correlation functions for handling correlations across levels of qualitative factors. Two examples are used to demonstrate the advantages of SKQ in aggregating information from related response surfaces and metamodeling them simultaneously, in addition to maintaining SK's ability of effectively tackling the impact of simulation errors.