Controlling the conditional false alarm rate for the MEWMA control chart

Abstract

An integral part of the design of control charts, including the multivariate exponentially weighted moving average (MEWMA) control chart, is the determination of the appropriate control limits for prospective monitoring. Methods using Markov chain analyses, integral equations, and simulation have been proposed to determine the MEWMA chart limits when the limits are based on a specified in-control average run length (ARL) value. A drawback of the usual approach is that the conditional false alarm rate (CFAR) for these charts varies over time in what might be in an unexpected and undesirable way. We define the CFAR as the probability of a false alarm given no previous false alarm. We do not condition on the results of a Phase I sample, as done by others, in studies of the effect of estimation error on control chart performance. We propose the use of dynamic probability control limits (DPCLs) to keep the CFAR constant over time at a specified value. The CFAR at any time, however, could be controlled to be any specified value using our approach. Using simulation, we determine the DPCLs for the MEWMA control chart being used to monitor the mean vector with an assumed known variance-covariance matrix. We consider cases where the sample size is both fixed and time-varying. For varying sample sizes, the DPCLs adapt automatically to any change in the sample size distribution. In all cases, the CFAR is held closely to a fixed value and the resulting in-control run length performance follows closely to that of the geometric distribution.

Keywords:

• Average run length
• dynamic probability control limits
• exponentially weighted moving average
• multivariate quality control
• statistical process monitoring

Additional information

Notes on contributors

Burcu Aytaçoğlu

Dr. Burcu Aytaçoğlu is an assistant professor in the Department of Statistics at Ege University, İzmir, Turkey. She received her BS from the Department of Statistics, Middle East Technical University (METU) and MSc degree both from the Department of Statistics and Department of Industrial Engineering, METU. After working as a production planning engineer in the automotive industry for about 6 years in İzmir, she received her PhD in Statistics from Ege University in 2013. Her research interests are statistical inference, statistical process control, process capability, and control charts.

Anne R. Driscoll

Dr. Anne R. Driscoll is an Associate Collegiate Professor in the Department of Statistics at Virginia Tech. She received her PhD in Statistics from Virginia Tech. Her research interests include statistical process control, design of experiments, and statistics education. She is a member of ASQ and ASA.

William H. Woodall

Dr. William H. Woodall is an emeritus professor in the Department of Statistics at Virginia Tech. He is a former editor of the Journal of Quality Technology (2001–2003). He is the recipient of the Box Medal (2012), Shewhart Medal (2002), Hunter Award (2019), Youden Prize (1995, 2003), Brumbaugh Award (2000, 2006), Bisgaard Award (2012), Nelson Award (2014), Ott Foundation Award (1987), and best paper award for IIE Transactions on Quality and Reliability Engineering (1997). He is a Fellow of the American Statistical Association, a Fellow of the American Society for Quality, and an elected member of the International Statistical Institute.