Homogeneously weighted moving average control chart based on Bayesian theory

Abstract

AbstractThe frequentist approach‐based control charts (CCs) have been widely used to monitor the performance of the process. As compare to frequentist approach, the CCs based on the Bayesian approach can be used with a small phase‐I dataset. This paper aims to propose a new homogenously weighted moving average CC based on the Bayesian theory. We have used two different loss functions, symmetric loss function as squared error loss function and asymmetric loss function as linex loss function under the informative prior as conjugate prior and noninformative prior by using posterior distribution (P dist) and posterior predictive distribution (PP dist). We calculated the values of average run length and standard deviation of run length to check the performance of the proposed homogenously weighted moving average CC based on the Bayesian theory. We also compared the proposed CC with the exponentially weighted moving average CC under the Bayesian theory. The results revealed that the proposed CC is more sensitive in the detection of small/moderate shifts than the considered CC. Finally, we presented an example based on a real‐life data for implementation purposes.