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Nested Plans as Sequential Quality Control Schemes for Detecting a Change in a Multivariate Normal Distribution

Abstract In the present paper we consider the problem of sequential quality control and propose nested plans for the quick detection, with low false alarm rate, of a change in a stochastic system. The nested plan includes two phases: a variable plan and an attributes plan. For the proposed nested plans we evaluate the exact (non-asymptotic) expressions for the in-control and out-of-control mean and the standard deviation of the run length. We especially consider the example where the initial and the final distributions are multivariate normal with different parameters and show that for many practical situations the speed of detection of a change using our proposed procedure is comparable with that of CUSUM detection schemes.