On progressive hybrid censored exponential distribution

Abstract

In this paper, we introduce a new adaptive Type-I progressive hybrid censoring scheme, which has some advantages over the progressive hybrid censoring schemes already discussed in the literature. Based on an adaptive Type-I progressively hybrid censored sample, we derive the exact distribution of the maximum-likelihood estimator (MLE) of the mean lifetime of an exponential distribution as well as confidence intervals for the failure rate using exact distribution, asymptotic distribution, and three parametric bootstrap resampling methods. Furthermore, we provide computational formula for the expected number of failures and investigate the performance of the point and interval estimation for the failure rate in this case. An alternative simple form for the distribution of the MLE under adaptive Type-II progressive hybrid censoring scheme proposed by Ng et al. [Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme, Naval Res. Logist. 56 (2009), pp. 687–698] is obtained. Finally, from the exact distribution of the MLE, we establish the explicit expression for the Bayes risk of a sampling plan under adaptive Type-II progressive hybrid censoring scheme when a general loss function is used, and present some optimal Bayes solutions under four different progressive hybrid censoring schemes to illustrate the effectiveness of the proposed method.

Keywords:

• Bayes risk
• maximum-likelihood estimation
• progressive hybrid censoring
• simulated annealing optimization
• variable sampling plan

Acknowledgements

We express our sincere thanks to the editor, the associate editor and the referee for their useful suggestions which led to an improvement over an earlier version of this manuscript. The first author thanks the National Science of Council of Taiwan (NSC Grant Number 99-2118-M-032-011-MY3) for funding this research.