相依屏蔽数据下双参数指数部件的可靠性分析  

Two-Parameter Exponential Component's Reliability Analysis Using Dependent Masked Data

作　　者：师义民[1] 顾昕[1] 孙天宇[1] 孙玉东[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《西北工业大学学报》2013年第1期29-33,共5页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(71171164;70471057);西北工业大学创业种子基金(Z2013153)资助

摘　　要：当串联系统含有屏蔽数据且屏蔽概率与失效部件相关时,讨论系统中双参数指数部件的可靠性估计问题。在定数截尾场合下,通过给定的屏蔽概率比,推导出双参数指数部件参数和可靠性指标的极大似然估计。鉴于极大似然估计法在完全屏蔽情形下的局限性,利用贝叶斯方法,在平方损失函数下推导出部件参数和可靠性指标的贝叶斯估计。最后利用随机模拟方法对估计结果进行验证,分析不同屏蔽概率比对极大似然估计精度的影响,并在无信息先验和共轭先验分布情形下,比较了贝叶斯估计的效果。To our knowledge, there is no paper in the open literature dealing with the subject mentioned in the ti- tle. Therefore, we analyze the reliability of two-parameter exponential components in a series system where the masked data and masking probability are dependent on failure components. With the given masking probability ratio, we derive the maximum likelihood estimation （MLE） of the parameters of two-parameter exponential compo- nents and that of the reliability index. Since the MLE has its limitations when the data are completely masked, we employ the squared error loss function to perform the Bayes estimation of the unknown parameters of two-parameter exponential components and their reliability indexes. Finally we carry out the numerical calculation of the mean square error of various estimated values to analyze the influence of different masking probability ratios on the accura- cy of the MLE and to compare the effects of the Bayes estimation under no-information prior distribution and con- junctional prior distribution respectively. The calculation results, given in Tables 2 and 3 and Fig. 1, and their a- nalysis show preliminarily that the mean square error of Bayes estimation under conjunctional prior distribution is less than that under non-informative prior distribution.

关 键 词：相依屏蔽数据 屏蔽概率比 可靠性分析 贝叶斯估计 双参数指数部件 

分 类 号：O213.2[理学—概率论与数理统计]