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A new methodology is proposed in this paper to both monitor an overall mean shift and classify the states of a multivariate quality control system. Based on the Bayesian rule (Montgomery, Introduction to statistical quality control, 5th edn. Wiley, New York, USA, 2005), the belief that each quality characteristic is in an out-of-control state is first updated in an iterative approach and the proof of its convergence is given. Next, the decision-making process of the detection and classification the process mean shift is modeled. Numerical examples by simulation are provided in order to understand the proposed methodology and to evaluate its performance. Moreover, the in-control and...