Distribution-free Phase II Mann–Whitney control charts with runs-rules

Abstract

The addition of runs-rules has been recommended to improve the performance of classical, normal theory Shewhart-type control charts, for detecting small to moderate size shifts. In this paper, we consider adding both standard and improved runs-rules to enhance the performance of the distribution-free Phase II Shewhart-type chart based on the well-known Mann–Whitney statistic proposed by Chakraborti and Van de Wiel [1]. Standard runs-rules are typically of the form w-of-(w + v) with w > 1 and v ≥ 0, and the improved runs-rules scheme is a combination of the classical 1-of-1 runs-rule and the w-of-(w + v) runs-rules. The improved scheme improves the performance of the charts in detecting larger shifts while maintaining its performance in detecting small to moderate shifts. The in-control and out-of-control performance of the proposed runs-rules enhanced distribution-free charts are examined through extensive simulations. It is seen that the proposed charts have attractive performance compared to some competing charts and are better in many cases. An illustrative example is provided, along with a summary and conclusions.