A Distribution-Free Shewhart Quality Control Chart Based on Signed-Ranks

• Activity Number: 238
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Quality & Productivity
• Author(s): Saad T. Bakir*+
• Companies: Alabama State University
• Keywords: ARL ; Nonparametric ; Ranks ; Signed ; Wilcoxon

Abstract

Since their inception by Walter Shewhart, most control charts have been distribution-based procedures where the process is assumed to follow a specified probability distribution (normal for continuous measurements). Due to Deming's influence and their wide adoption as basic tools of TQM, control charts have been applied to management processes where data may be markedly non-normal. We propose a distribution-free (nonparametric) quality control chart for monitoring a process center. The proposed chart is of the Shewhart type and is based on the signed-ranks of grouped observations. An advantage of this chart is that the in-control average run length and the false alarm rate do not depend on the process underlying distribution as long as that distribution is continuous and symmetrical. The exact in-control average run length of the proposed chart can be computed exactly using the null distribution of the Wilcoxon signed-rank statistic. Studies show that the proposed chart is more efficient than the X-bar chart under heavy-tailed distributions (the double exponential and the Cauchy), but is less efficient under light-tailed distributions (the uniform and the normal).