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.