Performance comparison for the CRL control charts with estimated parameters for high-quality processes

The conforming run length (CRL) control charts based on Bernoulli data have been shown to be effective when monitoring the proportion nonconforming rate, especially for high-quality processes. Considering the usage simplicity in practice, the count of conforming chart, RL2 chart and the geometric cumulative sum (CUSUM) chart are subject matter of this paper. When implementing the CRL control charts, the in-control proportion nonconforming rate is seldom known and accurate estimation is needed. Thus, we investigate the effects of parameter estimation on the CRL control charts using the average number of observations to signal and the standard deviation of the average number of observations to signal with a Bayes estimator. The SDANOS values of the CRL control charts show that practitioners should rarely expect in-control performance close to that obtained under the assumption when the process parameters are known. By comparing in-control performance of the CRL control charts, the geometric CUSUM chart is most sensitive to the parameter estimation.