Monitoring the process location by using new ranked set sampling-based memory control charts

ABSTRACT

The process monitoring and construction of control charts involves the measurement of the quality characteristic under certain time and cost constraints. Ranked set sampling (RSS) is a very useful and inexpensive method of obtaining a more representative sample when the actual quantification of sampling units is expensive or destructive, while the ranking of the observations is easier. In this paper, RSS and its variation, extreme RSS, median RSS and neoteric RSS are employed to construct new memory type homogeneously weighted moving average (HWMA) control charts to monitor the process location. The HWMA chart assigns a particular weight to the most recent sample, while all the previous samples are assigned an equal proportion of the remaining weight. The run length properties of the proposed control charts are studied by using extensive Monte Carlo simulations. The performance of the proposed charts is compared with the simple random sampling-based exponentially weighted moving average (EWMA) and HWMA besides RSS-based EWMA counterparts. The comprehensive comparisons established the better shift detection ability of the proposed control charts. To demonstrate the practical implementation of the proposed charts, a real industrial dataset is used which also confirms the better mean shift detection ability of the proposed charts.

KEYWORDS:

• Exponentially weighted
• homogeneous weights
• median ranked
• neoteric ranked set sampling
• process monitoring

Acknowledgments

The authors are thankful to the editor and anonymous referees for their valuable comments which led to improvement of the paper. The first author expresses his gratitude to Chinese Scholarship Council (CSC), People’s Republic of China for providing the support and excellent research facilities.

Nomenclature

Table

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research work is partially funded by the National Natural Science Foundation of China under the Grant Number (11531001).

Notes on contributors

Tahir Nawaz

Tahir Nawaz obtained his MSc and MPhil degrees in Statistics from the Islamia University Bahawalpur, Pakistan and Government College University Lahore, Pakistan respectively. He served as a Statistical Officer in Punjab Bureau of Statistics during May 2007 to November 2009. He served as a Lecturer in Statistics in the Islamia University Bahawalpur, Pakistan during November 2009 to October 2013. He is working as a Lecturer in the Department of Statistics, Government College University Faisalabad, Pakistan since November 2013. Currently, he is pursuing his PhD (Statistics) from the School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, People’s Republic of China under the Chinese Government Scholarship Program (2016). His research interest includes Statistical Process Control, Distribution Theory, and Survey Sampling.

Dong Han

Dong Han obtained his master’s degree in probability and statistics in 1985 from Central South University, People’s Republic of China. He earned his PhD in probability and statistics from Beijing Normal University, People’s Republic of China in 1989. He served in the Department of Mathematics at the Xinjiang University, People’s Republic of China from 1989 to 2000. He joined School of Mathematical Sciences, Shanghai Jiao Tong University, People’s Republic of China in 2000 and currently working as a professor. He has many refereed publications in Annals of Statistics, Journal of American Statistical Association, Statistica Sinica, Journal of Applied Statistics, Journal of Statistical Physics, etc. His research interest includes Statistical Process Control, Mathematical Models in Finance, Random Graphs and Complex Networks.