Knowing the time of changes in mean and variance in a process is crucial for engineers to identify the special cause quickly and correctly. Because assignable causes may give rise to changes in mean and variance at the same time, monitoring the mean and variance simultaneously is required. In this paper, a mixture likelihood approach is proposed to detect shifts in mean and variance simultaneously in a normal process. We first transfer the change point model formulation into a mixture model and then employ the expectation and maximization algorithm to estimate the time of shifts in mean and variance simultaneously. The proposed method called EMCP (expectation and maximization change point) can be used in both phase I and II applications without the knowledge of in-control process parameters. Moreover, EMCP can detect the time of multiple shifts and simultaneously produce the estimates of shifts in each individual segment. Numerical data and real datasets are employed to compare EMCP with the direct statistical maximum likelihood method without the use of mixture models. The experimental results show the superiority and effectiveness of the proposed EMCP. The outperformance of EMCP in detecting the time of small shifts is particularly important and beneficial for engineers to identify assignable causes rapidly and accurately in phase II applications in which small shifts occur more often and hence lead to a large average run length.
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