A processed monitored with an X chart is considered. It may go out of control due to the occurrence of one of several independent assignable causes. After the process has gone out of control and the assignable cause has been determined, the process undergoes improvement that results in a reduction of the rate due to that cause. A Bayesian estimator of the rate at which the process is going out of control as well as of the rates of the individual assignable causes is developed. The estimation procedure makes use of the Markov chain Monte Carlo technique of data augmentation. Numerical illustrations are provided that indicate how the posterior results depend upon both the data and the choice of the parameters of the prior distributions.
