A compound exponential distribution with application to control charts

In this paper, we propose a compound model based on the exponential distribution with its scale parameter randomized. Several mathematical properties of this new model are derived. By assuming that the quantitative characteristic of interest is distributed according to the proposed model, a new control chart is developed with the necessary measures for the control chart obtained using the belief estimator. We provide an application of the control chart to a real data set associated with health care system. In terms of the average run length, the proposed chart performs better than some existing charts. Furthermore, Monte Carlo simulations were performed to examine how the maximum likelihood estimators perform with regard to estimating parameters of the proposed model. The results indicate that the performance of the maximum likelihood estimators is reasonable.