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The competing risks problem is ubiquitous in different areas of life science, in engineering and science where failure of one component causes to fail all the system. Studying life testing experiment of a product or material, usual requires long period of time to monitoring. For the purpose of reducing the testing period, test units may be presented under conditions more severe than normal circumstances, which is called accelerated life tests (ALTs). More precisely, this procedure makes the lives shorter than would be spotted or monitored under normal conditions. Burr XII model has increasingly important in engineering statistics than other model. So, within this paper, maximum likelihood and Bayesian estimations will be discussed under the type-II censored Burr XII life time data. The Burr XII parameters as well as accelerated factor under competing risks model will be estimated. Also, the asymptotic confidence intervals under normality theory and credible intervals are obtained from MCMC sampling method will be drawn. Finally, the maximum likelihood and Bayesian estimations will be considered and a simulation investigation is described and reported by comparing the two approaches. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we investigate the problem of point and interval estimations for the modified Weibull distribution (MWD) using progressively type-II censored sample. The maximum likelihood (ML), Bayes, and parametric bootstrap methods are used for estimating the unknown parameters as well as some lifetime parameters (reliability and hazard functions). Also, we propose to apply Markov chain Monte Carlo (MCMC) technique to carry out a Bayesian estimation procedure. Bayes estimates and the credible intervals are obtained under the assumptions of informative and noninformative priors. The results of Bayes method are obtained under both the balanced squared error loss (bSEL) and balanced linear-exponential (bLINEX) loss. We show that these loss functions are more general, which include the MLE and both symmetric and asymmetric Bayes estimates as special cases. Finally, Two real data sets have been analyzed for illustrative purposes. [Copyright &y& Elsevier]

In this paper, we consider the analysis of Burr XII distribution based on the competing risks model under progressive Type-II censoring, where the amount of units withdrawn at each stage is assumed to be random and subject to a binomial distribution. The maximum likelihood estimations of unknown parameters are derived and their existence and uniqueness are proved as well. Furthermore, approximate confidence intervals are also constructed by using the observed Fisher information matrix and delta method. Moreover, Bayes estimators and associated credible intervals under different loss functions are obtained based on MCMC method. In addition, simulation study used to evaluate the performance of all estimators proposed is included. Finally, a practical data example is given to illustrate all the inferential processes developed here. [ABSTRACT FROM AUTHOR]