| It is known that for some types of production processes, control charts based on the probabilities that the process is out of control can yield lower expected false alarm rates and expected times to signal than conventional charts such as the cumulative sum (these charts are called Bayesian charts). However, there has been no systematic investigation of how estimation of the production process parameters affects the performance of Bayesian charts. Since for most control chart implementations, production parameters are estimated from an in-control sample in Phase I, it is important to study the effect of this estimation.;This study aims to evaluate the performance of the Bayesian control chart (for monitoring changes in the process mean) with estimated parameters. The metrics that are used to measure the control chart performance are EFA (expected number of false alarms) and ARL1 (average out of control run length). Monte Carlo simulations are performed to estimate the conditional and the marginal run length distributions. Comparisons are made to the performance of cumulative sum charts with estimated parameters. Also, recommendations are made on the number of samples to be used to generate estimates in Phase I of Bayesian control chart implementation. |
