A Nonparametric Procedure for Process Control Based on Within-Group Ranking

Abstract

A nonparametric procedure is developed for the problem of quickly detecting any shift in the mean of a sequence of observations from a specified control value. The proposed procedure is based on Wilcoxon signed-rank statistics where ranking is within groups. A cumulative sum control chart type stopping rule is used with the Wilcoxon statistics. Using a Markov chain approach, the average run length of the procedure can be computed exactly for any distribution for which the distribution of the Wilcoxon signed-rank statistic is known. The procedure has the same average run length for any continuous distribution which is symmetric about the control value.