A Control Chart for Gamma Distributed Variables Using Repetitive Sampling Scheme

Nasrullah Khan, Muhammad Aslam, Liaquat Ahmad, Chi-Hyuck Jun

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.

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DOI: http://dx.doi.org/10.18187/pjsor.v13i1.1390

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Title

A Control Chart for Gamma Distributed Variables Using Repetitive Sampling Scheme

Keywords


Description

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.

Date

2017-03-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 13 No. 1, 2017



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810