Alternative Designs of the Hodges-Lehmann Control Chart

Abstract

The Hodges-Lehmann control chart was proposed as a nonparametric alternative to the classical control chart. The proposed technique for establishing control limits produces control charts with in-control average run lengths (ARL0s) quite different from the anticipated ARL0s. In this paper two alternative methods for obtaining a Hodges-Lehmann control chart with a specific ARL0 are provided. The first alternative modifies the method of constructing the control limits and the second alternative modifies the statistic plotted. A numerical example of the three control charts is provided. The alternative control charts and the control chart are compared in their robustness to changes in distributional form.

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