Nonparametric progressive sign chart for monitoring process location based on individual data

ABSTRACT

Statistical process control (SPC) plays a vital role in the maintenances and improvements of quality outputs in manufacturing, industrial and service production processes. Control chart is an important SPC tool, used to detect noises and to improve process performance. When the underlying process distribution lacks the assumption of normality, nonparametric (NP) control charts become essential and particularly are useful because their in-control (IC) run length properties remain the same for every continuous distribution. This article develops the NP progressive mean sign (NPPM-SN) chart for monitoring the process target through 100% inspection by taking individual measurements from the process. The performance of the proposed NPPM-SN chart is examined under zero-state and steady-state scenarios. The IC and out-of-control run length properties of the proposed control chart are evaluated using Monte Carlo simulation. The proposed NPPM-SN chart is compared with traditional exponentially weighted moving average (EWMA), nonparametric EWMA sign (NPEWMA-SN) and traditional progressive mean (PM) control charts based on individual measurements using average run length and some other characteristics of the run-length distribution. The proposed NPPM-SN chart is found more robust (for all distributions) and efficient (for skewed distributions) as compared to its competitors. Along with a real-life example related to high voltage power supply, a simulated data example is also presented for the implementation of the proposed NPPM-SN chart.

KEYWORDS:

• Average run length
• control chart
• individual measurements
• nonparametric
• progressive mean
• robustness
• sign statistic

Acknowledgements

The authors are grateful to the editor and referees for their constructive comments that led to substantial improvements in the article. The author Muhammad Riaz is indebted to the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia, for providing excellent research facilities.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Zameer Abbas

Zameer Abbas obtained his MSc in Statistics from the University of Punjab Lahore in 2007 with distinction and MPhil in statistics from university of Sargodha, Pakistan in 2017. He joined Punjab Higher Education Department as Lecturer in 2009 and is presently serving as Assistant Professor at Government Ambala Muslim College Sargodha. The areas of his research interests include statistical inference, statistical quality control and non-parametric techniques.

Hafiz Zafar Nazir

Hafiz Zafar Nazir obtained his MSc and MPhil degrees in Statistics from the Department of Statistics, Quaid-i- Azam University, Islamabad, Pakistan, in 2006 and 2008, respectively. He did his PhD in statistics from the Institute of Business and Industrial Statistics University of Amsterdam, The Netherlands, in 2014. He served as a lecturer in the Department of Statistics, University of Sargodha, Pakistan, during 2009 to 2014. He is now serving as an assistant professor in the Department of Statistics, University of Sargodha, Pakistan, from 2015 to date. His current research interests include statistical process control, nonparametric techniques, and robust methods.

Muhammad Abid

Muhammad Abid obtained his MSc and MPhil degrees in statistics from Quaid-i-Azam University, Islamabad, Pakistan, in 2008 and 2010, respectively. He did his PhD in statistics from the Institute of Statistics, Zhejiang University, Hangzhou, China, in 2017. He served as a statistical officer in National Accounts Wing, Pakistan Bureau of Statistics (PBS) during 2010 to 2011. He is now serving as an Assistant Professor in the Department of Statistics, Government College University, Faisalabad, Pakistan, from 2017 to present. His research interests include statistical quality control, Bayesian statistics, nonparametric techniques, and survey sampling.

Noureen Akhtar

Noureen Akhtar obtained her MSc and MPhil degrees in statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan, in 2004 and 2007, respectively. She served as a lecturer in the Department of Statistics, University of Sargodha, Pakistan, during 2009 to 2013. She is now serving as an assistant professor in the Department of Statistics, University of Sargodha, Pakistan, from 2013 to date. Her current research interests include experimental design, statistical process control, and regression analysis.

Muhammad Riaz

Muhammad Riaz obtained his PhD in statistics from the Institute for Business and Industrial Statistics, University of Amsterdam, The Netherlands, in 2008. He holds the position of professor in the Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. His current research interests include statistical process control, nonparametric techniques, and experimental design.