A progressive mean control chart for dispersed count data considering tail behavior

ABSTRACT

Popular discrete distributions generally neglect tail behavior in the count data despite its significance in many industrial and non-industrial processes. The generalized Conway-Maxwell-Poisson (GCOMP) distribution considered the tail behavior while modelling the dispersed count data. In this study, GCOMP distribution-based progressive mean control chart is developed to monitor ‘over-dispersed and longer tail’ or ‘under-dispersed and shorter tail’ count data and termed as the GPM control chart. Performance evaluation based on the run-length (RL) distribution for the proposed control chart is conducted through the Monte Carlo simulation. The performance comparison shows that the proposed GPM control chart outperforms the progressive mean control chart based on the Conway-Maxwell-Poisson distribution (COMP-PM) for a range of shifts considered in ‘over-dispersed and longer tail’ count data, and for upwards shifts in ‘under-dispersed and shorter tail’ count data. The sensitivity of the Poisson distribution-based progressive mean control chart is also studied and compared with the proposed GPM control chart. It has been found that the proposed GPM control chart is very robust for ‘over-dispersed and longer tail’ or ‘under-dispersed and shorter tail’ count data. Finally, two simulated and numerical examples from finance and telecommunication engineering are used for the demonstration of the proposed control chart.

KEYWORDS:

• GCOMP distribution
• control charts
• average run length
• count data
• progressive mean

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Fakhar Mustafa

Fakhar Mustafa received his BSc in Statistics from Government College University, Lahore, Pakistan in 2013 and MS in Statistics from COMSATS Institute of Information Technology, Lahore, Pakistan in 2015. He is currently pursuing PhD degree in Statistics at the University of the Punjab, Lahore, Pakistan. His research interests include statistical process control, probability distribution and count data analysis.

Rehan Ahmad Khan Sherwani

Rehan Ahmad Khan Sherwani received his MPhil and PhD in Statistics from the University of the Punjab, Pakistan. He is currently working as a Full Professor in the College of Statistical Sciences, University of the Punjab, Lahore. He has numerous publications in peer-reviewed national and international research journals. His areas of specialisation include regression analysis, multilevel models, structural equation models, mixed models, and their applications.

Muhammad Ali Raza

Muhammad Ali Raza obtained his MSc and MPhil in Statistics from the University of the Punjab Lahore, Pakistan. He received 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 in 2015. His research interests include statistical process control and applied statistics.