Simulation optimization using stochastic kriging with robust statistics

Metamodels are widely used as fast surrogates to facilitate the optimization of simulation models. Stochastic kriging (SK) is an effective metamodeling tool for a mean response surface implied by stochastic simulation. In SK, it is usually assumed that the experimental data are normally distributed and uncontaminated. However, these assumptions can be easily violated in many practical applications. This paper proposes a new type of SK for simulation models that may have non-Gaussian responses; this new SK uses robust estimators of location (or central tendency) and scale (or variability) that are well-known in the literature on robust statistics. Statistical properties of the robust estimators used in this paper are briefly analyzed and the performances of the proposed methods are compared through numerical examples of different features. The comparison results show that the proposed robust SK with the robust estimators is quite efficient, no matter whether the standard assumptions hold or not.