In this paper, we construct a Bayesian framework combining Type-Ⅰ progressively hybrid censoring scheme and competing risks which are independently distributed as exponentiated Weibull distribution with one scale parameter and two shape parameters. Since there exist unknown hyper-parameters in prior density functions of shape parameters, we consider the hierarchical priors to obtain the individual marginal posterior density functions,Bayesian estimates and highest posterior density credible intervals. As explicit expressions of estimates cannot be obtained, the componentwise updating algorithm of Metropolis-Hastings method is employed to compute the numerical results. Finally, it is concluded that Bayesian estimates have a good performance.
In a reliability comparative test, the joint censoring model is usually adopted to evaluate the performances of units with the same facility. However, most researchers ignore the pos- sibility that there is more than one factor for the failure when a test unit fails. To solve this problem, we consider a joint Type-II hybrid censoring model for the analysis of exponential competing failure data. Based on the maximum likelihood theory, we compute the maximum likelihood estimators （MLEs） of parameters and then obtain the condition ensuring MLEs existence for every unknown parameter. Then we derive the conditional exact distributions and corresponding moment properties for parameters by the moment generating function （MGF）. A Monte-Carlo simulation is conducted to compare the performances of different ways. And finally, we conduct a numerical example to illustrate the proposed method.
在具有随机移走的逐步增加Ⅱ型截尾试验模型下,利用极大似然和Bayes方法分别给出了某航天器电源系统部件的参数和可靠性估计,并利用Tierney and Kadane近似和Gibbs抽样算法解决了Bayes估计中高维积分的计算问题。最后通过仿真实例对某航天器电源系统进行可靠性评估,并将各估计结果进行比较,验证了本文估计方法的可行性和有效性。
