Phase - II Lepage - type CUSUM charts for joint monitoring of location and scale

Abstract

Most control charts in nonparametric statistics tend to focus on detecting changes in the location or scale parameters. Since it is ideal to monitor both, researchers have proposed to combine them into a single statistic. From there, the Lepage-type family of tests was born, and it’s been updated with many versions. Chowdhury, Mukherjee, and Chrakaborti proposed merging the Ansari-Bradley and Wilcoxon Rank Sum tests into a single plotting statistic able to track persistent changes in the location and scale parameters in Phase II in the form of a CUSUM chart, using a reference sample from Phase I. The work from Guerrero (2016) based on several tests proposed by Conover et al. (1981) shows that there may be many statistics able to perform better than the Ansari-Bradley for monitoring the scale parameter. In the present work, we propose three Control charts based on the mentioned recommendations. These are the LP-M, LP-FK, and LP-SR CUSUM charts, in which the Ansari-Bradley statistic is replaced for the Mood, the Fligner and Killeen, and the Squared ranks tests respectively. Via Monte Carlo simulations, Control limits are tabulated for practitioners, plus the In-control and Out-of-control performance of the charts are calculated and compared with the CUSUM-Lepage Chart proposed by Chowdhury. This will help to choose the most useful CUSUM chart for each scenario. An example using real data illustrates how the proposed Control Charts must be implemented.