Designing a Degradation Test with a Two-Parameter Exponential Lifetime Distribution

Abstract

Degradation testing (DT) is a useful approach to assessing the reliability of highly reliable products which are not likely to fail under the traditional life tests or accelerated life tests. There have been a great number of excellent studies investigating the estimation of the failure time distribution and the optimal design (e.g., the optimal setting of the inspection frequency, the number of measurement, and the termination time) for DTs. However, the lifetime distributions considered in the studies mentioned above are all those without failure-free life. Here, failure-free life is characterized by a threshold parameter below which no failure is possible. The main purpose of this article is to deal with the optimal design of a DT with a two-parameter exponential lifetime distribution. More specifically, with respect to a DT where a linearized degradation model is used to model the degradation process and the lifetime is assumed to follow a two-parameter exponential distribution, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal combination of the inspection frequency, the sample size, and the termination time are determined by minimizing the mean squared error of the estimated 100p-th percentile of the lifetime distribution of the product. An example is provided to illustrate the proposed method and the corresponding sensitivity analysis is also discussed.

Keywords:

• Degradation test
• Failure-free life
• Highly reliable product
• Two-parameter exponential distribution

Mathematics Subject Classification:

• Primary 62-07
• Secondary 60E99

Acknowledgments

This work was partially supported by the National Science Council (Grant No. NSC-99-2221-E-151-024; NSC-102-2623-E-001-001-ET) of Taiwan, Republic of China.