Distribution-free cumulative sum and exponentially weighted moving average control charts based on the Wilcoxon rank-sum statistic using ranked set sampling for monitoring mean shifts

ABSTRACT

Whenever a practitioner is not sure about the underlying process distribution, alternative monitoring schemes that may be used are called nonparametric charts. A nonparametric scheme mostly used to monitor the difference in the means of two samples is called the Wilcoxon rank-sum (WRS). In this paper, we propose nonparametric (or distribution-free) cumulative sum and exponentially weighted moving average charts based on the WRS using ranked set sampling. We thoroughly discuss the performance of the proposed control charts in terms of run-length properties through intensive simulations. Moreover, we conduct an overall performance comparison using the relative mean index and a variety of quality loss functions (for instance, the average extra quadratic loss, average ratio of the average run-length and performance comparison index). The newly proposed charts have very attractive run-length properties and they have better overall performance than their counterparts. An illustrative example is given, as well as an easy-to-use table with optimal design parameters to aid practical implementation.

KEYWORDS:

• Distribution-free control charts
• case U
• balanced ranked set sampling
• median ranked set sampling
• run-length distribution
• overall performance measures

AMS SUBJECT CLASSIFICATION:

• 93C83
• 68U20
• 62D05
• 62G30
• 62H10
• 62P30

Acknowledgements

They also thank Dr Marien Graham from the University of Pretoria for her helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jean-Claude Malela-Majika http://orcid.org/0000-0001-7236-7678

Additional information

Funding

The authors thank the University of South Africa for the support.