An adaptive Bayesian scheme for joint monitoring of process mean and variance

This paper presents a new model for the economic optimization of a process operation where two assignable causes may occur, one affecting the mean and the other the variance. The process may thus operate in statistical control, under the effect of either one of the assignable causes or under the effect of both assignable causes. The model employed uses the Bayes theorem to determine the probabilities of operating under the effect of each assignable cause. Based on these probabilities, and following an economic optimization criterion, decisions are made on the necessary actions (stop the process for investigation or not) as well as on the time of the next sampling instance and the size of the next sample. The superiority of the proposed model is estimated by comparing its economic outcome against the outcome of simpler approaches such as Fp (Fixed-parameter) and adaptive Vp (Variable-parameter) Shewhart charts for a number of cases. The numerical investigation indicates that the economic improvement of the new model may be significant.