Nonparametric CUSUM and EWMA Control Charts for Detecting Mean Shifts

Abstract

Nonparametric control charts are useful when the underlying process distribution is not likely to be normal or is unknown. In this paper, we propose two nonparametric analogs of the CUSUM and EWMA control charts based on the Wilcoxon rank-sum test for detecting process mean shifts. We first derive the run-length distributions of the proposed control charts and then compare the performance of the proposed nonparametric charts to (1) CUSUM and EWMA control charts on subgroup means and (2) the median chart and the Shewhart-type nonparametric control chart based on Mann–Whitney test. We show that the charts proposed herein perform well in detecting step mean shifts and perform almost the same as the parametric counterparts when the underlying process output follows a normal distribution and better when the output is nonnormal. We also study the effect of the reference sample size and the subgroup size on the performance of the proposed charts. A numerical example is also given as an illustration of the design and implementation of the proposed charts.