Estimating the Out-of-Control Rate from Control Chart Data in the Presence of Multiple Causes and Process Improvement

Abstract

We consider a process that is monitored with an X chart. The process 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. We develop 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. The estimation procedure makes use of the Markov chain Monte Carlo technique of data augmentation. We provide numerical illustrations that indicate how the posterior results depend upon the data and upon the choice of the parameters of the prior distributions.