Bayesian variable selection in Kriging metamodeling for quality design

The increasing complexity of production processes and rapid developments in digital technology have fueled the adoption of metamodels in quality design. Kriging has emerged as one of the most popular emulation methods for both deterministic and stochastic simulations. Conventional Kriging models with predetermined mean functions, such as ordinary or universal Kriging, may exhibit subpar predictive performance when strong trends exist. This paper proposes a novel variable selection procedure for the mean function that ensures prediction accuracy while using only a limited number of variables to capture the potential existing trends in deterministic simulations. The proposed method integrates the benefits of Bayesian variable selection and frequentist statistical tests. Initially, a group of potential models is chosen to build the mean function, employing the Bayesian method with priors designed to guarantee sparsity. This results in a significant reduction in the number of models to be considered in the next stage. Subsequently, each candidate model undergoes rigorous frequentist tests to thoroughly assess its reliability and validity. Extensive simulation studies are conducted using the well-known Borehole function and a real-life case. The results demonstrate the superiority of the proposed method over several existing approaches, establishing its effectiveness in achieving robust parameter design.