A critique of a variety of “memory-based” process monitoring methods

Abstract

Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart. In addition, new schemes have been proposed based on alternative weighting of past data, usually to put greater emphasis on past data and less weight on current and recent data. In other cases, the output of one process monitoring method, such as the EWMA statistic, is used as the input to another method, such as the CUSUM chart. Often the recursive formula for a control chart statistic is itself used recursively to form a new control chart statistic. We find the use of these ad hoc methods to be unjustified. Statistical performance comparisons justifying the use of these methods have been either flawed by focusing only on zero-state run length metrics or by making comparisons to an unnecessarily weak competitor.

Keywords:

• Control chart
• cumulative sum (CUSUM) chart
• exponentially weighted moving average (EWMA) chart
• mixed control charts
• statistical process monitoring

Additional information

Notes on contributors

Sven Knoth

Dr. Sven Knoth is a professor of Statistics in the Department of Mathematics and Statistics within the School of Economic and Social Sciences at the Helmut Schmidt University, Hamburg, Germany. Prior to that, he worked as a Senior SPC Engineer at Advanced Mask Technology Center (AMTC) Dresden, Germany, from 2004 to 2009. He is an Associate Editor of Computational Statistics and Quality Engineering.

Nesma A. Saleh

Dr. Nesma A. Saleh is an Assistant Professor of Statistics at the Department of Statistics, Faculty of Economics and Political Science, Cairo University. She holds her B.Sc. (2009), M.Sc. (2012), and PhD (2016) in statistics from Cairo University. Her main area of interest is statistical quality control.

Mahmoud A. Mahmoud

Dr. Mahmoud A. Mahmoud is the Dean of the Faculty of Economics and Political Science, Cairo University. Prior to becoming Dean, he was the Vice Dean for Education and Students’ Affairs, and a Professor of Statistics at Cairo University, Faculty of Economics and Political Science. He holds his BS (1992) and MS (1997) in statistics from Cairo University, and PhD (2004) in statistics from Virginia Tech - USA. His primary area of interest is statistical quality control and improvement. He is a member of the Editorial Board of Quality and Reliability Engineering International, and Review of Economics and Political Science (REPS). He is a Deputy Editor-in-Chief in Journal of Humanities and Applied Social Sciences (JHASS).

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.

Víctor G. Tercero-Gómez

Dr. Víctor G. Tercero-Gómez is a professor at the Department of Industrial Engineering, in the School of Engineering and Sciences at Tecnologico de Monterrey. Certified Black Belt and Master Black Belt in Six Sigma. His research interests include SPM, nonparametric statistics and quality engineering.