Nonparametric Control Charts to Jointly Monitor Scale and Location Parameters

Abstract

Conventional Shewhart control chart works efficiently on many assumptions. The most important one is data should be normally distributed. But in many processes, we observed, process outcomes do not follow normal distribution. On another side nonparametric statistics works on very few assumptions. It does not require any knowledge regarding probability distribution of population under study. Also, to check process is under statistical control or not we need to draw two separate charts, chart for mean and chart for dispersion. But many statistics had been developed by researchers to jointly monitor location and scale parameters. To jointly monitor location and scale parameters without assuming distribution of parent population, in this article different non-parametric control charts based on Wilcoxon-Mood, Wilcoxon-Ansari Bradley, Wilcoxon-Siegel-Tukey, Wilcoxon-Conover Signed rank have been discussed. The performance of these charts under different distributions and sample sizes to control both parameters simultaneously, Monte Carlo simulations had been used.