Robustness of the EWMA Control Chart to Non-normality for Autocorrelated Processes

Abstract

Most commonly used control charts for monitoring quality characteristics of the processes were developed under the assumption that the observations are randomly sampled from a normal population. It is well known that these control charts have more false alarms than usual when processes are positively autocorrelated. One remedy is to adjust the control limits such that the modified control charts can achieve an about right false-alarm rate. In this paper, we investigate the robustness of such modified individuals Shewhart control chart and modified exponentially weighted moving average (EWMA) control chart to the usual normality assumption of the white noise term in an AR(1) process with positive autocorrelation. The performances of the control charts under study are evaluated on the basis of the average run length (ARL) curves. It is found that the modified EWMA control chart is more robust to the normality assumption than the modified individuals Shewhart control chart in terms of the in-control ARL for some heavy-tailed symmetric distributions and some skewed distributions. Results also show that the choice of the EWMA smoothing parameter A is very crucial to the ARL performance. However, choosing an appropriate value for λ is not easy and many practitioners may simply choose a value of 0.1 or 0.2, which are values commonly suggested for the standard EWMA charts designed for independent normal data. Unfortunately, the modified EWMA control chart with these popular values of λ does not perform well enough for some of the positively autocorrelated non-normal data in our study. In a preliminary study for improving the robustness, we consider two control charts with data averaging schemes called the moving-average EWMA chart and subgroup-average EWMA chart, respectively. A small simulation study shows that the subgroup-average EWMA control chart with the same naïve choice of λ = 0.1 or 0.2 indeed outperforms the modified EWMA control chart with a tradeoff of slight inefficiency on the detecting power for the case under study.