A Shewhart-type nonparametric multivariate depth-based control chart for monitoring location

Abstract

Parametric multivariate control charts like Hotelling’s rely on certain distributional assumptions that if these assumptions are not met, it leads us to an excessive number of false alarms and reduces the effectiveness of the monitoring strategy. In contrast, nonparametric multivariate control charts, specifically data-depth-based charts and related inferences, do not require any distributional assumptions and no constraints on data dimensions. In this paper, based on a family of multivariate affine invariant distribution-free data-depth-based tests for the multivariate one-sample location problem, a Shewhart-type nonparametric multivariate phase-II control chart is proposed. The performance of the proposed control chart is evaluated with a Monte Carlo simulation study using the average run length measure and is compared to that of competitors. It is observed that the proposed control chart maintained a desirable performance and leads to quicker detection of shifts. It is also a close competitor to Hotelling’s chart when the underlying distribution of the process is bivariate normal. Moreover, it performs better than its nonparametric competitor under the bivariate non-normal elliptical direction class of distributions, specifically heavy-tailed, light-tailed, and t-distributions, in a variety of settings. The control chart procedure is illustrated as an application to real-life data.