One-sided Control Charts Based on Precedence and Weighted Precedence Statistics

In this paper, we study one‐sided control charts based on precedence statistics. Because we focus on the problem of detecting ‘smaller’ lifetime than expected, we consider only one‐sided control charts that have not received much attention in the literature. Alarm rate and average run length are derived when the process is in control and also when the process is out of control for two Lehmann alternatives. On the basis of the alarm rate and average run length, we propose suitable randomized procedures to determine the best precedence control chart. Control charts based on weighted precedence statistics are then studied. The charts developed here are illustrated with coal mining disasters data. Finally, a comparison of the performance of these two charts is made with that of a Wilcoxon–Mann–Whitney control chart and a cumulative sum chart based on the precedence statistic, and some conclusions are drawn.