Abstract
The Bayesian approach has been used as an effective framework in tracking the process mean and detecting the random occasional jump on the control chart X-, R.This approach make an estimation of the posterior distribution of the process mean based on its prior distribution and the set of past observations. In contrary to previous research, in this paper, we develop a Bayesian approach for tracking and updating the posterior distribution of the process mean where it is subject to random changes with dynamic prior probability of occurrence.To update this prior probability in each new observation, we used numerical integration based on the set of past observations. We assume a general model of process, where the observations are represented as a process mean plus a random error term. The performance of this model is investigated and compared to the performance of the posterior distribution chart [9] where the prior probability of the change's occurrence is stable over time. The results demonstrate the effectiveness of the proposed model. Indeed, the random jump, whatever its amplitude is large, medium or low, can be detected faster than in the case where the prior probability of change's occurrence is stable. Consequently the predictive distribution of the future observation is more precise. This work allows decision-makers to better anticipate the future evolution of the control chart process and optimize their planning for corrective and preventive actions.