Decision-making in detecting and diagnosing faults of multivariate statistical quality control systems

Abstract

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 out-of-control average run length (Montgomery, Introduction to statistical quality control, 5th edn. Wiley, New York, USA, 2005) of the proposed method are compared with the ones from the well-known Multivariate Cumulative Sum (MCUSUM), Multivariate Exponentially Weighted Moving Average (MEWMA) and Hotelling T2 methods in different scenarios of mean shifts. The results of the simulation study show that the proposed methodology performs better than other methods for all shifts of the process mean. Additionally, the estimated probabilities of making correct classifications by the proposed approach are encouraging.