An equivalence between multivariate cumulative sum control charts

Abstract

ABSTRACTWe show that an auxiliary information based (AIB) cumulative sum (CUSUM) chart is equivalent to a special case of the multivariate CUSUM control chart proposed by J. D. Healy. Due to this equivalence, the limitations and restrictions of the AIB-CUSUM chart also apply to Healy’s multivariate CUSUM chart.KEYWORDS: Auxiliary information-based (AIB) control chartCUSUM chartmultivariate statistical process controlstatistical process monitoring Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationNotes on contributorsNesma A. SalehNesma A. Saleh is an Associate 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. MahmoudMahmoud A. Mahmoud is the Vice President of Cairo University. Prior to this, he was the Dean of the Faculty of Economics and Political Science, Cairo University, 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. WoodallWilliam 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 the 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.