Estimation of the stress-strength parameter under two-sample balanced progressive censoring scheme

Abstract

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples.

Keywords:

• Bayesian inference
• joint censoring scheme
• maximum likelihood
• optimal censoring scheme
• stress-strength reliability
• Weibull distribution

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions which were helpful in improving the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).