A robust alternate to the HEWMA control chart under non-normality

ABSTRACT

In practice, a hybrid exponentially weighted moving average (HEWMA) control chart for monitoring the process mean based on the normality assumption. The performance of control chart is seriously affected if quality characteristics depart from normality or have the presence of outliers. For such situations, a new robust-HEWMA control chart is proposed for the scenario in which quality characteristics being monitored follow symmetric not necessarily normal as well as skewed phenomena. The generalized least-squares (GLS) algorithm based on order statistics is integrated to determine the control limits for non-normal process. Consequently, the process mean is unbiased and has the minimum variance in spite of non-normality. Moreover, for the long-tailed symmetric and skewed processes, the GLS estimators through their systematic coefficients structures provide robust estimates. To utilize this advantage, we have investigated the impact of data contamination and the estimators used in Phase I on the performance of proposed robust HEWMA control chart in the Phase II. Finally, we provide two real-life examples along with the simulation studies to show the implantation of our proposed chart.

KEYWORDS:

• Long-tailed symmetric process
• Burr distribution
• Lloyd’s estimators
• average run length
• robust HEWMA

Acknowledgments

We would like to thank anonymous referees and editor for their valuable comments to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Azaz Ahmed

Azaz Ahmed is a PhD student in the National College of Business Administration and Economics Lahore Pakistan. He gained his MPhil and MSc in Statistics from the Department of Statistics, University of the Punjab, Lahore, Pakistan. He is an Assistant Professor at the Govt. Islamia College railway road, Lahore Pakistan. His research interests are quality control charts and their applications, order random variable and Survey Sampling.

Aamir Sanaullah

Dr. Aamir Sanaullah has earned a doctoral degree in Statistics from National College of Business Administration and Economics Lahore Pakistan. He has an M.Phil degree in Statistics from GC University Lahore Pakistan, and Master in Statistics from University of Arid Agriculture Rawalpindi, Pakistan. Dr. Sanaullah is an HEC approved supervisor and currently serving for CUI Lahore Campus, as an Assistant Professor at Department of Statistics. His research interests are quality control charts and their applications, and Survey Sampling.

Muhammad Hanif

Muhammad Hanif is a professor and Pro Rector in the National College of Business Administration and Economics Lahore Pakistan. He received his PhD in Statistics from University of the Punjab Lahore Pakistan. His research interest is Survey sampling, Research Methods, Bio- Statistics, Statistical Inference, Quantitative Methods, Public Health, Operations Research, Demography and currently in Statistical Process Control.