A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution. 1. Introduction Most traditional statistical quality control charts assume that the monitored process has a prespecified known probability distribution (usually normal for continuous measurements). Consequently, the chart properties (control limits, false alarm rate, and the in-control average run length) would be in error if the process distribution were missspecified. To remedy this, a number of distribution-free (or nonparametric) schemes that maintain the same chart properties over a class of distributions have been proposed in the literature. For an overview of nonparametric control charts, see Chakraborti et al. [1, 2]. Another problem is that traditional control charts aim at monitoring a change in one parameter (usually a location or scale) of a process distribution. Realistically, however, when a special cause influences a process, it may cause a shift in more than one parameter (location, scale, skewness, etc.) of the process distribution. To remedy this, we need control charts designed to monitor a broad rather than a one-parameter change in a process distribution. To our knowledge, Bakir [3] was first to suggest such charts based on the two-sample Kolmogorov-Smirnov and the Cramer-von Mises statistics. Zou and Tsung [4] proposed a nonparametric likelihood ratio chart for monitoring broad changes in a process