Determination of warranty length for one-shot devices with Rayleigh lifetime distribution

Abstract

An important goal for the producers is to stimulate the purchase intention of consumers so that the profit can be increased. An attractive warranty policy can not only represent the quality of product but also enhance the purchase desire of consumers. A long warranty length usually stands for high quality. However, it is not suitable for the producers to provide an unlimited warranty length. The main purpose of this paper is to establish an approach to determine the optimal warranty length based on one-shot device sample. The one-shot device data are collected under a multiple-level constant-stress accelerated life test. The lifetime distribution at each stress level is assumed to be Rayleigh. A utility function is provided to measure the monetary profit based on a free-replacement warranty policy. The optimization problem is studied under the Bayesian framework. A numerical example is studied for illustrating purpose. Finally, the sensitivity analysis is performed to see the influence of some parameters on the optimal warranty length.

Keywords:

• Accelerated life test
• Bayesian approach
• one-shot device testing
• posterior predictive distribution
• utility function

Acknowledgements

The authors wish to thank the Associate Editor and referees for valuable suggestions which led to the improvement of this paper.

Additional information

Funding

The work of the first author was partially supported by the Ministry of Science and Technology of R.O.C. grant MOST-106-2118-M-032-005.