A study on a memory type EWMA control chart with unknown process parameters

Abstract

In this paper, the exponentially weighted moving average (EWMA) chart when the process parameters are unknown is studied. Under such circumstances, the process parameters are estimated from an in-control Phase-I dataset. Since the run length distribution of EWMA chart is skewed to the right, interpretation based on average run length (ARL) does not provide meaningful information about the chart's performance. On the contrary, the median run length (MRL) provides more useful interpretation. Thus, MRL will be used to assess the performance of the EWMA chart when process parameters are known and estimated. In this study, it is found that the out-of-control and in-control performances are severely affected by parameter estimation, especially when the sample size and process mean shifts are small. Moreover, a large number of in-control Phase-I samples is required so that the EWMA chart with estimated process parameters attains satisfactory performances as its known process parameters counterpart.