Control Chart Based on the Hodges-Lehmann Estimator

Abstract

A new variables control chart for location based on the Hodges-Lehmann estimator associated with the Wilcoxon signed rank statistic is presented. The proposed chart is nonparametric and hence maintains the nominal type I error specified. Calculations of control limits are simplified for certain conditions. The proposed approach compares favorably with the Shewhart control chart when the data are from a Gaussian distribution. Its performance is better than the traditional approach in the case of moderate sample sizes from long-tailed symmetric distributions. These properties make it well suited for early production runs of limited size when the distribution of the process statistic is unknown. The method may also be used to establish robust control limits.