Abstract
In practice, when the magnitude of a future mean shift is unknown, it is always desired to design a control chart to perform reasonably well over a range of shifts rather than to optimize the performance at detecting a particular level of shifts. Compared with the conventional cumulative sum (CUSUM) control chart designed based on a prespecified mean shift, the adaptive CUSUM (ACUSUM) chart proposed by Sparks (2000) can detect a broader range of mean shifts. This paper develops a two-dimensional Markov chain model to analyze the performance of ACUSUM charts. Moreover, a more general operating model is suggested for the current ACUSUM chart to simplify its implementation.
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