Dual CUSUM control schemes for detecting a range of mean shifts

Conventional quality control procedures, such as the CUmulative SUM (CUSUM) and exponentially weighted moving average charts are usually designed based on a mean shift with a given size. In practice, the exact value of the shift size is often unknown and can only be reasonably assumed to vary within a certain range. Such a range of shifts deteriorates the performance of existing control charts. In this paper, a quality control scheme, a Dual CUSUM (DCUSUM), is applied that combines two CUSUM charts to detect the range of shifts. The out-of-control signal is triggered if either one of the CUSUM statistics goes out of the DCUSUM control limits. In particular, a design procedure for the DCUSUM charts is developed and an analytical formula for the Average Run Length (ARL) calculation is obtained via the Markov chain method. The proposed DCUSUM charts are compared with the conventional CUSUM and combined Shewhart-CUSUM charts. Based on a proposed criterion, the integrated relative ARL, the proposed schemes show better performance in detecting a range of mean shifts.

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