New distribution-free memory-type control charts based on the Wilcoxon rank-sum statistic

ABSTRACT

In this paper, a new distribution-free double exponentially weighted moving average (DEWMA) control chart based on the Wilcoxon rank-sum (WRS) test without any distributional assumption of the underlying quality process is proposed. The proposed chart is the extension of the exponentially weighted moving average (EWMA) WRS control chart where the EWMA WRS statistic is applied twice. The ability of the EWMA and DEWMA WRS charts to detect small to large process mean shifts is further improved by combining each of them with the Shewhart control chart based on the WRS statistic. The in-control and out-of-control performances of the proposed charts are thoroughly investigated using extensive simulations. It is found that the proposed charts perform better than their competitors under both normal and non-normal distributions. A numerical illustration using real-life dataset is given in order to demonstrate the design and implementation of the new charts.

KEYWORDS:

• Combined Shewhart-DEWMA chart
• combined Shewhart-EWMA
• memory-type chart
• nonparametric DEWMA chart
• nonparametric EWMA chart
• Wilcoxon rank-sum test

Acknowledgments

The author thanks the reviewers for their valuable comments and suggestions that helped to improve the originally submitted manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Notes on contributors

Jean-Claude Malela-Majika

Jean-Claude Malela-Majika obtained his BSc (Hons) degree in Mathematical Statistics from the High Institute of Statistics, Honours and Master’s degrees in Statistics from the University of Pretoria and a PhD in Statistics from the University of South Africa. He is currently a senior lecturer at the University of South Africa and a member of the South African Statistical Association, the International Statistical Institute (ISI) and the Institute of Certificated and Chartered Statisticians of South Africa (ICCSSA). His principal research interests include Statistical Process / Quality Control and Statistical Inference.