Adaptive CUSUM control chart with variable sampling intervals

The standard cumulative sum chart (CUSUM) is widely used for detecting small and moderate process mean shifts, and its optimal detection ability for any pre-specified mean shift has been demonstrated by its equivalence to continuous sequential tests. In real practice, the assumption of knowing the true mean shift in prior cannot be always met. So it is desirable to design a procedure that is efficient for detecting a range of future expected but unknown mean shifts. Adaptive CUSUM control chart, which can continuously adjust itself by a one-step forecasting operator, has been proposed to detect efficiently and robustly for a range of mean shifts in the early literature. Moreover, in terms of sampling time to signal, control chart with the VSI (variable sampling intervals) feature can detect the process changes more quickly than the traditional FSI (fixed sample intervals) chart. In this paper, a new CUSUM control chart which is based on both adaptive and VSI features is discussed. Also, a two-dimensional Markov chain model is developed to evaluate its run-time performance.