Joint monitoring of mean and variance using likelihood ratio test statistic with measurement error

ABSTRACT

This paper explores the effect of measurement errors on a joint monitoring control chart by using three different techniques (i) covariate method (ii) multiple measurements (iii) linear increasing variance. The joint monitoring control chart in the presence of measurement errors are discussed by using an exponentially weighted moving average statistic in the generalized likelihood ratio (GLR) test statistic under ranked set sampling and pair ranked set sampling (PRSS) procedures. For this purpose, different out-of-control scenarios including mean shifts, variance shifts, and simultaneous shifts are discussed under the considered sampling schemes. The performance of the joint monitoring control chart is evaluated in terms of average run length (ARL) and the standard deviation of run length (SDRL) by conducting an extensive simulation study. The results show that PRSS procedure can reduce the adverse effect of measurement errors on the detection ability of joint monitoring control chart. An example is provided with real data set for the implementation of the joint monitoring control chart in the presence of measurement errors.

KEYWORDS:

• Joint monitoring
• measurement errors
• average run length
• ranked set sampling
• pair ranked set sampling

Acknowledgments

The authors are thankful to the reviewers for valuable comments that significantly improved the original version of the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Farah Arif

Farah Arif is a Ph.D. student of Statistics at the National College of Business Administration & Economics, Lahore, Pakistan. Her research interests are statistical quality control and survey sampling

Muhammad Noor-Ul-Amin

Muhammad Noor-ul-Amin received his Ph.D. degree from NCBA&E, Lahore, Pakistan. He has been working in various universities for teaching and research that includes the Virtual University of Pakistan, University of Sargodha, Pakistan, and the University of Burgundy, France. He is currently working as an Assistant professor at COMSATS University Islamabad-Lahore Campus. His research interests include sampling techniques and control charting techniques. He is an HEC approved supervisor

Muhammad Hanif

Muhammad Hanif completed his Master's degree from New South Wales University, Australia in Multistage Cluster Sampling. He completed his Ph.D. in Statistics from the University of Punjab, Lahore, Pakistan. He has more than 40 years of research experience. He is an author of more than 200 research papers and 10 books. He has served as a Professor in various parts of the world i.e. Australia, Libya, Saudi Arabia, and Pakistan. He is presently a Professor of Statistics and Vice-Rector (Research) at NCBA & E, Lahore, Pakistan