Statistical process control of multistage processes with Bayesian sequential bifurcation

Multistage process quality control has received much attention in the last two decades. In this article, we provide a statistical quality control scheme for multistage processes based on the state space model and Bayesian theory. The posterior probabilities of each possible fault scenario are evaluated. Whenever the fault scenario associated with the largest posterior probability exceeds certain threshold, the control chart will give out an alarm. Numerical analysis proves that the new method has satisfactory diagnosis power. Besides, detailed derivation of the fault propagation pattern of the Kalman-filtered residuals in presence of mean shifts is also presented.