Nonparametric multivariate processes monitoring with guaranteed in-control performance for changes in location

Abstract

Multivariate statistical process control (MSPC) addresses the concurrent monitoring of several measurements. Since multivariate normality is rare in practice, nonparametric schemes become useful alternatives. Inspired by the development of distribution free Shewhart-type control charts to monitor multivariate data streams as a mean to address high-dimensional processes where distance measures are ranked and compared using two-sample test statistics, a novel distribution-free multivariate chart for location that combines Mahalanobis distances with the Mann-Whitney statistic is proposed. By considering, probably for the first time in nonparametric MSPC, practitioner-to-practitioner variation, we account for the uncertainty of the run length distribution, where computational complexity is addressed using the cumulative conditional false alarm probability as a proxy of the conditional average run length. This approach enables quicker determination of control limits that guarantee a minimum performance given a Phase-I sample, a common situation in parametric approaches, but scarcely discussed in nonparametric monitoring. Since no direct alternative exists, results are compared with the traditional approach to show the benefits of a guarantee in-control performance with comparable sensitivity when dealing with medium to large shifts. An implementation is illustrated in a real scenario related to Wine Quality Data.