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Abstract
The study proposes a cumulative quantity control chart, based on the mixture of two components Weibull model, namely MWQ-chart. The design structure of the proposed chart is developed by using the cumulative quantity examined between non-conformities (Q) as the charting statistic. The performance of the proposed MWQ-chart is evaluated in terms of some popular measures like average run length and average length of inspection. The cumulative quantity control chart is discussed as a special case. An extension of the proposal is also suggested in the form of MWQr-chart based on the cumulative quantity between non-conformities until r nonconformities happened in one or both components of the mixture model. The implementation of the proposed chart is also shown on a dataset for practical demonstration.
Additional information
Notes on contributors
Zaheer Ahmed
Zaheer Ahmed obtained M.Phil degree in Statistics from Department of Statistics, Quaid-i-Azam University Islamabad, in 2013. His current research interests include Bayesian Statistics, Statistical Process Control and Mixture Modeling.
Muhammad Aslam
Muhammad Aslam is former Professor and Chairman, Department of Statistics, Quaid-i-Azam University Islamabad, Pakistan. Presently, He is serving as Professor of Statistics in Department of Basic Sciences, Riphah International University Islamabad, Pakistan. He obtained his M.Sc. is Statistics from University of the Punjab Lahore, Pakistan, in 1978 and Ph.D. in Bayesian Statistics from University of Wales UK in 1996. His research interest includes in Bayesian Statistics, Mathematical Statistics, Bayesian Quality Control and application of Bayesian Statistics in Paired Comparison models. He has number of publications in Statistical journals of International repute.
Muhammad Riaz
Muhammad Riaz obtained Ph.D. in statistics from the Institute for Business and Industrial Statistics, University of Amsterdam, The Netherlands, in 2008. He holds the position of Associate 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.
Nasir Abbas
Nasir Abbas is serving as Assistant Professor at Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. He got his Ph.D. in Industrial Statistics from the Institute for Business and Industrial Statistics, University of Amsterdam, The Netherlands, in 2012. He also served as Assistant Census Commissioner in Pakistan Bureau of Statistics during July 2011 — January 2013. His current research interests include Quality Control particularly control charting methodologies under parametric and nonparametric environments.