Some quasi-distribution-free schemes for Phase-I analysis of multivariate industrial processes

Abstract

This paper introduces distance-based quasi-distribution-free approaches for Phase-I analysis of multivariate and high-dimensional processes. Phase-I analysis involves a retrospective study of the collected data to learn the features and stability of the process. At this stage, knowledge about the underlying distribution is limited and nonparametric statistical process monitoring (NSPM) plays a vital role. A wide range of NSPM tools exist for Phase-I analysis of univariate data, but similar schemes for multivariate and high-dimensional data are relatively limited. In particular, the multivariate NSPM literature related to monitoring the location and scale aspects in tandem in Phase I is scarce, but it is crucial in evaluating and establishing process stability. This paper aims to bridge the gap by introducing alternative multivariate schemes that are capable of detecting changes in the multivariate location vector, scale matrix, or both without knowledge of the process distribution. A thorough Monte Carlo experiment is conducted for comparative performance evaluation, and the results are encouraging in favour of the proposed schemes. Guidelines on using the proposed schemes are also offered. Finally, two industrial case studies are reported.