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Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics
Authors:N. Balakrishnan  I.S. Triantafyllou  M.V. Koutras
Affiliation:1. McMaster University, Hamilton, Ontario, Canada;2. University of Piraeus, Piraeus, Greece
Abstract:In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.
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