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AbstractThis paper is concerned with a constant-stress partially accelerated life test (CSPALT) model whose items are allocated at either normal use condition or under accelerated use condition. The lifetimes of items are assumed to follow Burr-X distribution based on Type-I hybrid censoring scheme. Two methods of estimation namely, E-Bayesian and Bayesian estimation methods are used for estimating the distribution parameter and the acceleration factor. These estimates are derived by using LINEX and squared error loss (SEL) functions. To obtain estimates of Bayesian and E-Bayesian methods, Markov chain Monte Carlo (MCMC) method is used. For illustration, a real-life data set is presented and applied to the CSPALT model. In the end, a comparison between proposed methods is carried out to investigate the performance of methods.

In this paper, Burr-X distribution with Type-II hybrid censored data is considered. The E-Bayesian estimation (the expectation of the Bayesian estimate) and the corresponding Bayesian and maximum likelihood estimation methods are studied for the distribution parameter and the reliability function. Bayesian and E-Bayesian estimates are obtained under LINEX and squared error loss functions. By applying the Markov chain Monte Carlo techniques, Bayesian and E-Bayesian estimates are obtained. Also, confidence intervals of maximum likelihood estimates, as well as credible intervals of Bayesian and E-Bayesian estimates, are constructed. Furthermore, a numerical example of a real-life dataset is provided for the purpose of illustration. Finally, a comparison among the E-Bayesian, the Bayesian and the maximum likelihood methods is presented.

SYNOPTIC ABSTRACTThis article deals with Bayesian and E-Bayesian (expectation of the Bayesian estimate) estimation methods of the parameter and the reliability function of Burr-X distribution based on a generalized Type-I hybrid censoring scheme. Bayesian and E-Bayesian estimates are obtained under LINEX and squared error loss functions. By applying Markov chain Monte Carlo techniques, Bayesian and E-Bayesian estimates based on a generalized Type-I hybrid censoring scheme are derived. Also, credible intervals for Bayesian and E-Bayesian estimates are computed. Examples of generalized Type-I hybrid censored samples and real data sets are presented for the purpose of illustration. Finally, a comparison between Bayesian and E-Bayesian estimation methods is conducted.

The constant-stress partially accelerated life test (CSPALT) model with Type-II hybrid censoring scheme (Type-II HCS) is the subject of our research. Units have a lifetime that follows the generalized Rayleigh distribution. Bayesian and E-Bayesian estimates are derived by applying two of the loss functions, mainly the squared error loss (SEL) and LINEX loss functions. Bayesian and E-Bayesian estimates are obtained using Markov chain Monte Carlo (MCMC) methods. To prove the applicability and the importance of the subject, a test for real data will be provided. To evaluate the distribution’s effectiveness, we utilized a variety of datasets and proposed several kinds of censoring. Finally, all results are compared in order to determine the effectiveness of the proposed methods. All major findings are concluded in the conclusion section.