Nonparametric cost‐minimized Shewhart‐type process monitoring with restricted false alarm probability

Abstract

Abstract Traditional Duncan‐type models for cost‐efficient process monitoring often inflate type I error probability. Nevertheless, controlling the probability of type I error or false alarms is one of the key issues in sequential monitoring of specific process characteristics. To this end, researchers often recommend economic‐statistical designs. Such designs assign an upper bound on type I error probability to avoid excessive false alarms while achieving cost optimality. In the context of process monitoring, there is a plethora of research on parametric approaches of controlling type I error probability along with the cost optimization. In the nonparametric setup, most of the existing works on process monitoring address one of the two issues but not both simultaneously. In this article, we present two distribution‐free cost‐efficient Shewhart‐type schemes for sequentially monitoring process location with restricted false alarm probability, based, respectively, on the sign and Wilcoxon rank‐sum statistics. We consider the one‐sided shift in location parameter in an unknown continuous univariate process. Nevertheless, one can easily extend our proposed schemes to monitor the two‐sided process shifts. We evaluate and compare the actual performance of the two monitoring schemes employing extensive computer simulation based on Monte Carlo. We investigate the effects of the size of the reference sample and the false alarm constraint. Finally, we provide two illustrative examples, each based on a realistic situation in the industry.

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