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.

Key Words:

• AR(1) model
• autocorrelated processes
• average run length
• control charts
• modified EWMA chart
• modified individuals Shewhart chart
• robustness to non-normality
• subgroup-average EWMA chart

Additional information

Notes on contributors

Jyh-Jen Horng Shiau

Jyh-Jen Horng Shiau He is a Professor in the Institute of Statistics at National Chiao Tung University, Taiwan. She received her BS in mathematics from National Taiwan University, MS in applied mathematics from the University of Maryland Baltimore County, MS in computer science and Ph.D. in statistics from the University of Wisconsin-Madison. Formerly, she taught at Southern Methodist University, the University of Missouri at Columbia, and National Tsing Hua University and worked for the Engineering Research Center of AT&T Bell Labs before she moved to Hsinchu, Taiwan. Her research interests include industrial statistics and non-parametric function estimation. She is a member of the Institute of Mathematical Statistics and a lifetime member of the International Chinese Statistical Association.

Hsu Ya-Chen

Ya-Chen Hsu He received her BS degree in mathematics from National Chung Cheng University and MS degree in statistics from National Chiao Tung University, Taiwan. Currently, she is a Ph.D. student in the Department of Industrial Engineering & Management at National Chiao Tung University, Taiwan. Her research interests include statistical quality control and process capability analysis. Most of this research was conducted while she was a graduate student in the Institute of Statistics at National Chiao Tung University under the supervision of the first author.