Two Nonparametric Control Charts for Detecting Arbitrary Distribution Changes

TLDR

Traditional control charts assume knowledge of the pre‑change distribution, an assumption that is often unrealistic when data are scarce, and existing nonparametric Phase II charts typically detect only location shifts. The study aims to develop nonparametric Phase II charts that can detect arbitrary changes in the process distribution without assuming a specific form. The authors construct two distribution‑free charts by embedding the Kolmogorov–Smirnov and Cramér–von Mises tests within a change‑point model framework.

Abstract

Most traditional control charts used for sequential monitoring assume that full knowledge is available regarding the prechange distribution of the process. This assumption is unrealistic in many situations, where insufficient data are available to allow this distribution to be accurately estimated. This creates the need for nonparametric charts that do not assume any specific form for the process distribution, yet are able to maintain a specified level of performance regardless of its true nature. Although several nonparametric Phase II control charts have been developed, these are generally only able to detect changes in a location parameter, such as the mean or median, rather than more general changes. In this work, we present two distribution-free charts that can detect arbitrary changes to the process distribution during Phase II monitoring. Our charts are formed by integrating the omnibus Kolmogorov–Smirnov and Cramer—von-Mises tests into the widely researched change-point model framework.