A Control Chart for Gamma Distribution using Multiple Dependent State Sampling

• Aslam, Muhammad (Department of Statistics, Faculty of Sciences, King Abdulaziz University) ;
• Arif, Osama-H. (Department of Statistics, Faculty of Sciences, King Abdulaziz University) ;
• Jun, Chi-Hyuck (Department of Industrial and Management Engineering, POSTECH)
• Accepted : 2016.09.27
• Published : 2017.03.30
• 123 27

Abstract

In this article, a control chart based on multiple dependent (or deferred) state sampling for the gamma distributed quality characteristic is proposed using the gamma to normal transformation. The proposed control chart has two pairs of control limits, which can be determined by considering the in-control average run length (ARL). The shift in the scale parameter of a gamma distribution is considered and the out-of-control ARL is evaluated. The performance of the proposed chart has been shown for different levels of the parameters of the proposed control chart. It is also shown that the proposed chart is better than the Shewhart chart in terms of ARLs. A case study with a real data has been included for the practical usage of the proposed scheme.

Keywords

Multiple Dependent states;Control Chart;Gamma Distribution;Wilson-Hilferty Transformation;Average Run Length;Simulation

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