A Distribution-Free Multivariate Phase I Location Control Chart for Subgrouped Data from Elliptical Distributions

<div><p>In quality control, a proper Phase I analysis is essential to the success of Phase II monitoring. A literature review reveals no distribution-free Phase I multivariate techniques in existence. This research develops a Phase I location control chart for multivariate elliptical processes. The resulting in-control reference sample can then be used to estimate the parameters for Phase II monitoring. Using Monte Carlo simulation, the proposed method is compared with the Hotelling's <i>T</i>² Phase I chart. Although Hotelling's <i>T</i>² chart is preferred when the data are multivariate normal, the proposed method is shown to perform significantly better under nonnormality. This article has supplementary material online.</p></div

Nonparametric (distribution-free) control charts : an updated overview and some results

Control charts that are based on assumption(s) of a specific form for the underlying process distribution are referred to as parametric control charts. There are many applications where there is insufficient information to justify such assumption(s) and, consequently, control charting techniques with a minimal set of distributional assumption requirements are in high demand. To this end, nonparametric or distribution-free control charts have been proposed in recent years. The charts have stable in-control properties, are robust against outliers and can be surprisingly efficient in comparison with their parametric counterparts. Chakraborti and some of his colleagues provided review papers on nonparametric control charts in 2001, 2007 and 2011, respectively. These papers have been received with considerable interest and attention by the community. However, the literature on nonparametric statistical process/quality control/monitoring has grown exponentially and because of this rapid growth, an update is deemed necessary. In this article, we bring these reviews forward to 2017, discussing some of the latest developments in the area. Moreover, unlike the past reviews, which did not include the multivariate charts, here we review both univariate and multivariate nonparametric control charts. We end with some concluding remarks.https://www.tandfonline.com/loi/lqen20hj2020Science, Mathematics and Technology Educatio