A study on the variable sampling interval EWMA X chart when the process parameters are unknown

The exponentially weighted moving average (EWMA) X chart is well known in statistical process control for detecting small and moderate process mean shift. A variablesampling-interval (VSI) control scheme of the EWMA X chart is able to enhance the speed of detection when the process is out-of-control as the intervals switch according to the value of the previous sample statistics. Generally, the performance of the VSI EWMA X chart is investigated under the assumption of known process parameters. However, in reality, these parameters are usually unknown and are estimated from a historical Phase-I dataset. Hence, the performance of the VSI EWMA X chart is significantly affected when the process parameters are unknown. This is due to estimation errors. In this paper, we investigate the effects of parameter estimation on the performance of the VSI EWMA X chart in terms of the average time to signal and standard deviation of the time to signal. Suggestions on the required number of Phase-I samples and sample sizes in designing the VSI EWMA X chart with unknown process parameters, are provided for practitioners' fast implementation.