Economic design of repetitive group sampling plan based on truncated life test under Birnbaum–Saunders distribution

Abstract

In this paper, we design the repetitive group sampling plan under Birnbaum–Saunders distribution, since this distribution is considered as an appropriate and flexible distribution to model different types of data particularly lifetime data. In this study, the Birnbaum–Saunders distributed mean lifetime of the product is considered as the quality characteristic where the shape parameter is assumed to be known. For different mean ratios, the design parameters such as sample size, conditional and unconditional acceptance numbers of the proposed repetitive group sampling plan are determined using the approach of two points on the operating characteristic curve. In order to select the optimal parameters, tables are constructed for different values of shape parameter of Birnbaum–Saunders distribution. We explain the implementation of the proposed repetitive group sampling plan with descriptive example as well as using real time data and the effect of misspecification of shape parameter on lot acceptance probability is investigated. In addition, the proposed repetitive group sampling plan is compared with single and double sampling plans in terms of discriminating power and average sample number. An economic design of the proposed repetitive group sampling plan is discussed and optimal plans are determined to satisfy both producer’s and consumer’s risks with minimum cost. Sensitivity of the proposed plan based on failure probability and cost parameters is analyzed in this paper.

Keywords:

• Birnbaum–Saunders distribution
• Consumer’s risk
• Producer’s risk
• Repetitive group sampling plan
• Truncated life test

Mathematics Subject Classification:

• 62D05
• 90B25
• 62P30

Acknowledgements

The authors are thankful to the Editor and the anonymous reviewers for their constructive comments which significantly improved the presentation of this manuscript. The first and second authors would like to thank Kalasalingam Academy of Research and Education for the financial support through the research fellowship.