Reevaluating the performance of control charts based on ranked-set sampling

Abstract

Nearly one hundred types of control charts have been proposed that incorporate ranked-set sampling (RSS) methods. The performance of these charts has been evaluated with comparisons to existing charts based on simple random sampling. The reduction of the standard error in estimating the parameter being monitored with RSS leads to uniformly better average run length performance. We show, however, that these performance comparisons can be very misleading once the sampling strategy over time is considered more carefully with the benefits of RSS being considerably overstated. We consider the most basic RSS method when monitoring the mean of the process, but the approach can be applied to evaluate other RSS monitoring methods.

Keywords:

• average run length
• control chart
• data aggregation
• ranked-set sampling
• statistical process control
• statistical process monitoring

Disclosure statement

The authors report there are no competing interests to declare.

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.

Abdul Haq

Abdul Haq is an Associate Professor at the Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan. His research interest is in Statistical Process 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).

Nesma A. Saleh

Nesma 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.