Analysis of two Weibull populations under joint progressively hybrid censoring

Abstract

Joint Type-I progressive hybrid censoring scheme has been proposed to terminate the life-test experiment at maximum time that the experimenter can afford to continue. This article deals with the problem of estimating the two Weibull population parameters with the same shape parameter under joint Type-I progressively hybrid censoring scheme on the two samples using maximum likelihood and Bayesian inferential approaches. Using Fisher information matrix, the two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are developed using squared-error loss function. Since the Bayes estimators cannot be expressed in closed forms, hence, Gibbs within Metropolis-Hastings algorithm is proposed to carry out the Bayes estimates and also to construct the corresponding credible intervals. Moreover, some popular joint censoring plans are generalized and can be obtained as a special cases from our results. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To determine the optimal progressive censoring plan, two different optimality criteria are considered. Finally, to show the applicability of the proposed methods in real phenomenon, a real-life data set is analyzed.

Keywords:

• Bayesian estimation
• joint Type-I progressively hybrid censoring
• maximum likelihood estimation
• Markov chain Monte Carlo techniques
• optimum censoring scheme
• Weibull distribution

Mathematics Subject Classification(2010)::

• 62F10
• 62F15
• 62N01
• 62N02
• 62N05

Acknowledgements

The authors would like to express thanks to the Editor-in-Chief Prof. N. Balakrishnan and anonymous referees for their constructive comments and suggestions, which significantly improved the paper.