Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

ABSTRACT

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.

KEYWORDS:

• Acceptable quality level
• average sample number
• life test
• limiting quality level
• mean lifetime ratio

Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their precious comments and suggestions which helped to improve the quality of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Department of Science and Technology-Science and Engineering Research Board (DST-SERB), Government of India, through the project (SR/S4/MS:790/12).