Exact Likelihood Inference for Two Exponential Populations Under Joint Progressive Type-II Censoring

Abstract

Comparative lifetime experiments are of great importance when the interest is in ascertaining the relative merits of two competing products with regard to their reliability. In this article, we consider two exponential populations and when joint progressive Type-II censoring is implemented on the two samples. We then derive the moment generating functions and the exact distributions of the maximum likelihood estimators (MLEs) of the mean lifetimes of the two exponential populations under such a joint progressive Type-II censoring. We then discuss the exact lower confidence bounds, exact confidence intervals, and simultaneous confidence regions. Next, we discuss the corresponding approximate results based on the asymptotic normality of the MLEs as well as those based on the Bayesian method. All these confidence intervals and regions are then compared by means of Monte Carlo simulations with those obtained from bootstrap methods. Finally, an illustrative example is presented in order to illustrate all the methods of inference discussed here.

Keywords:

• Bayes inference
• Bootstrap confidence intervals
• Confidence bounds
• Coverage probabilities
• Exponential distribution
• Joint progressive Type-II censoring
• Life-testing
• Likelihood inference
• Simultaneous confidence intervals

Mathematics Subject Classification:

• Primary 62E15, 62F10, 62F2 F
• Secondary 62N05

Acknowledgments

The first author expresses his sincere thanks to Zanjan University (Iran) for supporting his visit to McMaster University (Canada), during which time this research was carried out. The second author acknowledges the support of the Natural Sciences and Engineering Research Council of Canada for conducting this research.