A Shewhart‐type Control Scheme to Monitor Weibull Data without Subgrouping

Abstract

This study proposes a Shewhart control scheme to simultaneously monitor the shape parameter and the scale parameter of Weibull data without subgrouping. The proposed control scheme comprises two charts: the X chart and the moving‐ratio (MRa) chart. The X chart plots individual observations to detect the shift of the scale parameter by assuming that the shape parameter is in‐control. In contrast, the MRa chart plots moving ratios, the minimum of two consecutive Weibull data divided by the maximum of them, to detect the shift of the shape parameter. This study models the transition process of the proposed control scheme as a Markov chain to calculate two performance measures: the average number of observations to signal and the average run length. Performance analysis shows that the proposed control scheme is effective in detecting the shift of parameters, especially for the downward shift of the shape parameter. Finally, the implementation of the proposed control scheme is illustrated in two skewed data sets. Copyright © 2013 John Wiley & Sons, Ltd.

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