逐步增加Ⅰ型混合截尾试验下B-S部件的可靠性分析

Reliability analysis for B-S components under progressive hybrid Type-Ⅰ censoring test

在逐步增加Ⅰ型混合截尾试验下,利用最大期望(expectation maximization,EM)算法讨论了Birnbaum-Saunders(B-S)部件的参数及可靠度的估计问题。将B-S分布复杂的分布形式转换成较为简单的逆高斯分布和逆高斯分布倒数的等加权和形式,推导出逐步增加I型混合截尾中隐藏变量的后验密度,进而获得部件寿命参数和可靠度的极大似然估计和渐近置信区间。蒙特卡罗数值算例表明,简化后的B-S分布在逐步增加I型混合截尾试验方案中,EM算法经过较少迭代即达到收敛。同时,通过对数据情形I和情形Ⅱ下的估计结果分析,给出了较一般截尾试验方式更为丰富的结论,使得相应的统计结果更加全面和精确。

The estimators for the component parameters and reliability of Birnbaum-Saunders （B-S）distribution under the progressive hybrid Type Ⅰ censoring test are considered.B-S distribution is transferred to the mixture of inverse Gaussian and reciprocal of inverse Gaussian distribution with equal weight,and the posterior density function of potential variables and the pseudo log-likelihood function in progressive Type Ⅰ hybrid censoring are derived.In addition,the maximum likelihood estimation and asymptotic confidence interval for life parameters and reliability performance are obtained based on the pseudo log-likelihood function.The numerical example results of Monte-Carlo show that the expectation maximization （EM）algorithm has a better performance in convergence with fewer iteration steps for progressive hybrid Type-Ⅰ censoring,and more results of estimation are given compared with normal censoring by analysis of data Case Ⅰ and Case Ⅱ which get more accurate and complete statistical results.