逐步Ⅱ型截尾下屏蔽数据Burr Ⅻ串联系统的可靠性分析

Reliability Analysis for Burr Ⅻ Series System with Masked Data under Progressive Type-Ⅱ Censoring

假设串联系统由两参数BurrⅫ部件组成,两个参数均未知。在逐步Ⅱ型截尾试验下,基于屏蔽系统寿命数据,讨论了部件参数与可靠度函数的统计推断问题。利用极大似然理论及迭代方法,获得了部件参数及可靠度函数的极大似然估计,并给出了其渐近置信区间。鉴于极大似然估计法在完全屏蔽情形下的局限性,通过引入辅助变量并运用Gibbs抽样法,讨论了部件参数及可靠度函数的贝叶斯估计和最大后验密度置信区间。最后给出仿真算例,验证了本文方法的可行性和有效性。

Assume that the series system contains multiple s-independent components,and the lifetime of each component follows a Burr XII distribution with two unknown parameters.Based on progressive type-Ⅱ censored and masked system lifetime data,we discuss the statistical inference for the unknown parameters and the reliability function of system and component.Maximum likelihood estimates and the corresponding asymptotic confidence intervals are obtained by using the maximum likelihood（ML）theory.In view of the limitation of ML approach when the failure cause is completely masked,Bayesian approach incorporated with auxiliary variables and Gibbs sampling is developed for estimating the parameters,and Monte Carlo method is employed to construct the highest posterior density credible intervals.Finally,a simulated example is given to illustrate the feasibility and validity of the methods proposed in this paper.