Bayesian estimation of the rate at which a process, monitored by an X̄ chart, goes out of control

Abstract

This paper examines a process that is monitored by an X̄ chart. It is assumed that the process may go out of control due to the occurrence of any of several independent assignable causes. The time until each specific assignable cause occurs is exponential, but the distributional parameters of the various causes are unknown and are not necessarily identical. A Bayesian approach is used to estimate these parameters. The approach encompasses prior knowledge about the parameters as well as observations of the process, including when the out-of-control situation was detected and the associated assignable cause. Numerical illustrations are provided that indicate how the posterior results depend upon the choice of the parameters of the prior distributions.