A Control Chart for Gamma Distributed Variables Using Repetitive Sampling Scheme | [Pakistan Journal of Statistics and Operation Research • 2017]

Author(s):

1. Nasrullah Khan: Department of Statistics University of Veterinary & Animal Sciences, Lahore (Sub Campus, Jhang), Pakistan.

2. Muhammad Aslam: Department of Statistics Faculty of Science, King Abdulaziz University, Jeddah 21551, Saudi Arabia.

3. Liaquat Ahmad: Department of Statistics University of Veterinary & Animal Sciences, Lahore, Pakistan.

4. Chi-Hyuck Jun: Department of Industrial and Management Engineering POSTECH, Pohang, Republic of Korea.

Abstract:

In this manuscript, a control chart is designed when the quality characteristic of interest follows a gamma distribution using repetitive sampling. The Wilson-Hilferty approximation is used to transform the gamma distributed characteristic to a normal random variable. Two pairs of control limits are established and their control constants are determined by considering the specified in-control average run length (ARL). The out-of-control ARL is derived when the process is shifted in terms of the scale parameter of the Gamma distribution. The ARLs are presented for various values of the shape parameter according to process shift parameters. A simulated example is given to illustrate the proposed control chart.

Page(s): 47-61

DOI: DOI not available

Published: Journal: Pakistan Journal of Statistics and Operation Research, Volume: 13, Issue: 1, Year: 2017

Keywords:

Gamma Distribution , Normal distribution Control chart , WilsonHilferty transformation

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