Non-parametric progressive signed-rank control chart for monitoring the process location

Abstract

In every process of the manufacturing and service industry, there exist variations. Quality practitioners desire to avoid these variations to maintain and improve the quality level of products and services. The control charts are commonly applied under the assumption of normality, however, when the underlying assumption is not valid, nonparametric (NP) control charts become alternatives for quality engineers and practitioners. In this article, an NP progressive mean control chart based on Wilcoxon signed-rank statistic (NPPM-SR) has been proposed for prompt detection of shifts in the process target. The NPPM-SR chart proves in-control robust and much effective performance in spotting deviations in the process location for heavy-tailed and skewed distributions. The run-length distribution performance of the proposed NPPM-SR chart for some selected continuous symmetrical distributions; normal, t, Laplace, logistic and contaminated normal distributions are evaluated under zero- and steady states using average run length (ARL) and some other run-length characteristics. The proposed NPPM-SR chart is compared with existing NP counterparts such as; NP exponentially weighted moving average sign (NPEWMA-SN) chart, NP EWMA based on Wilcoxon signed-rank statistic (NPEWMA-SR) chart and NP cumulative sum based on Wilcoxon signed-rank statistic (NPCUSUM-SR) chart. For the comparative analysis, the parametric competitors such as; traditional EWMA (EWMA-$\overline{X}$) chart and Double EWMA-$\overline{X}$ (DEWMA-$\overline{X}$) control charts are also included in this study. The proposed NPPM-SR charting scheme under zero-state has been found efficient as compared to steady-state and its existing counterparts. The piston rings data and simulated data have been taken for the illustration of the proposal.

KEYWORDS:

• Average run length
• manufacturing process
• nonparametric control charts
• piston ring
• Wilcoxon signed-rank

MSC:

• 62G35
• 62Gxx
• 62P30
• 62Pxx

Acknowledgements

The authors are grateful to the editor and referees for their constructive comments that led to substantial improvements in the article. The author Muhammad Riaz is indebted to the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia, for providing excellent research facilities.

Disclosure statement

No potential conflict of interest was reported by the author(s).