Adaptive CUSUM chart with cautious parameter learning

The classic CUSUM chart assumes that the in-control (IC) mean and variance are known. In practice, these parameters are usually estimated from an IC Phase I sample. Recently, Capizzi and Masarotto proposed a cautious parameter learning scheme to incorporate Phase II IC observations in the estimation of the IC mean and variance to reduce the variation of conditional average run lengths (ARLs). In this paper, we develop a new cautious parameter learning scheme that can distinguish IC observations from out-of-control (OC) observations in the Phase II sample more effectively than Capizzi and Masarotto's scheme. As a result, our cautious parameter learning scheme can provide better estimation of the IC mean and variance. Combining the new cautious parameter learning scheme with an adaptive CUSUM chart, our proposed monitoring procedure is easy to implement, and is shown to have less variability in conditional ARLs and better overall performance for detecting different mean shifts than existing methods.