Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2012, Article ID 147520, 10 pages
http://dx.doi.org/10.1155/2012/147520
Research Article

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

College of Business Administration, Alabama State University, P.O. Box 271, Montgomery, AL 36101, USA

Received 7 May 2012; Revised 17 July 2012; Accepted 22 July 2012

Academic Editor: Xiaohu Li

Copyright © 2012 Saad T. Bakir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.