Implementing lifetime performance index of products with two-parameter exponential distribution

Abstract

The manufacturing industry has prioritised enhancing the quality, lifetime and conforming rate of products. Process capability indices (PCIs) are used to measure process potential and performance. The process capability is evaluated with product survival time and a longer lifetime implies a better process capability and a higher reliability. In order to save experimental time and cost, a censored sample arises in practice. In the case of product possessing a two-parameter exponential distribution, this study constructs a uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the type II right-censored sample. Then the UMVUE of the lifetime performance index is utilised to develop the new hypothesis testing procedure in the condition of known lower specification limit. Finally, two practical examples are illustrated to employ the testing procedure to determine whether the product is reliable.

Keywords:

• reliability
• reliability testing
• two-parameter exponential distribution
• censored sample
• UMVUE

Acknowledgements

We thank the associate editor and the referees for their suggestions and helpful comments in revising the article. This research was partially supported by the National Science Council, R.O.C. (Plan No. NSC 95-2118-M-415-001, NSC 96-2118-M-415-001 and NSC 97-2118-M-415-001-MY2).