Run sum X- control chart with estimated process parameters

The run sum X- control chart is usually investigated under the assumption of known process parameters. In practice, process parameters are rarely known and they need to be estimated from an in-control Phase I dataset. However, different practitioners use different numbers of Phase I samples to estimate the process parameters. As a result, the commonly used performance measure, ie, the average run length becomes a random variable. In this study, we present a run sum X- control chart with estimated process parameters and use the standard deviation of the average run length to evaluate the average of the average run length performance of the run sum X- chart when process parameters are estimated. Based on the standard deviation of the average run length criterion, the number of Phase I samples required by the estimated process parameter-based run sum X- chart to have an average of the average run length performance close to that obtained under the assumption of known process parameters is recommended.