Equivalences between multiple dependent state sampling, chain sampling, and control chart runs rules

Abstract

Multiple dependent state sampling (MDSS) is a feature that was recently proposed for acceptance sampling plans. In addition, it is increasingly recommended to use this technique, and its generalization, with quality control charts. In our paper, we show that the MDSS feature is an extension of chain sampling in acceptance sampling applications. In addition, we show that use of the MDSS feature with control charts is equivalent to the use of standard supplementary runs rules. Analytical methods based on Markov chains for determining the performance of control charts with runs rules can also be applied to MDSS acceptance sampling applications. Additionally, we provide a derivation approach for some of the formulas for the performance measures for the MDSS charts and point out some incorrect derivations.

Keywords:

• acceptance sampling
• average run length (ARL)
• chain sampling
• exponentially weighted moving average (EWMA) chart
• Shewhart control chart
• statistical process monitoring

Notes

1 Aslam, Khan, and Jun (2014) incorrectly stated in their article that the multiple dependent state sampling was introduced by Wortham and Baker (1976), while in fact Wortham and Baker (1976) proposed the multiple deferred state sampling. This error has appeared in other papers as well.

Additional information

Notes on contributors

William H. Woodall

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 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.

Nesma A. Saleh

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

Mahmoud A. Mahmoud is 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 for Journal of Humanities and Applied Social Sciences (JHASS).