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Abstract:
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Most of the currently available distribution-free Phase II control charts for monitoring process location assume that the underlying process distributions have the same shape. However, in many applications in practice this assumption may not hold or may be hard to verify. In this paper, we examine the impact of the violation of the underlying assumptions on the performance of the Phase II Shewhart-type charts based on the Mann-Whitney statistic. As a more practical alternative, we consider a new distribution-free Shewhart-type chart based on the Fligner-Policello (1981) statistic that can be used to monitor location with fewer assumptions on the shapes of the underlying distributions. Performance of the proposed chart is studied in a simulation study. In the end, we find that traditional Mann-Whitney Shewhart-type chart is less robust than our new chart and it cannot sustain a relatively high performance under the violation of the same shape assumption.
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