系统可靠性评估中的信息融合方法及应用

【作者】 柴建；

【导师】 师义民；

【作者基本信息】 西北工业大学 ， 应用数学， 2006， 硕士

【摘要】 本文综合运用Bayes、经验Bayes及多层Bayes理论,在产品具有多源验前信息的情况下,充分利用验前信息,并结合少量现场试验样本对系统可靠性进行了评估。接着研究了Bayes统计分析中利用验前信息的稳健性问题。同时通过数值仿真来说明应用过程和方法的正确性、合理性。 主要工作如下: 首先,在系统验前信息多源性的情况下,由不同的验前信息得到不同形式的验前分布,利用可信度加权法、相关函数法、极大似然法来融合系统可靠性验前信息,合理地确定了各验前分布在融合综合验前分布中的权重。 其次,讨论了多源验前信息情况下如何对产品的失效率进行融合估计的问题,利用经验Bayes及多层Bayes方法来融合系统的多源验前信息,得到了产品失效率的验前分布及后验分布,并分别在平方损失及Linex损失函数下得到产品失效率的经验Baves估计。 再次,讨论了经验Bayes和多层Bayes信息融合方法在k/n(G)系统可靠性评估中的应用,在多个验前信息源的情况下,得到了系统可靠性指标的Bayes估计。 最后,以平方损失下的Γ-后验期望损失为判别准则,讨论了指数寿命型产品失效率的最优Bayes稳健区间估计,导出了指数寿命型产品失效率的最优Bayes稳健点估计。更多还原

【Abstract】 In this paper, when there has few samples, we discuss the estimation of the system reliability in multi-sources of prior information with Bayes, EB (Empirical Bayes) and HB (Hierarchical Bayes) theories. Then we study the robustness of prior distribution in Bayes statistical analysis. The results from simulation show that the method proposed in this paper is effective and reasonable.The main workis:Firstly, When prior information comes from different sources.we develop some methods to realize the fusion of the system information based on the correlation function、 the credibility and the ideology of the maximum like hood. And confirm weights of every prior distribution logically when fusing.Secondly, methods for pooling failure rate data obtained from different sources is discussed, introduce how to use the EB and HB theories to realize the fusion information from multi-sources, and find the prior distribution and posterior distribution of the failure rate. Then the EB estimate of the failure rate is obtained using the squared error loss and the Linex loss functions.Thirdly, When prior information comes from different sources, the EB and HB fusion methods of prior information and their applications in reliability analysis of k/n (G) system are discussed, and then give the Bayes estimation.Finally, the optimal Bayes robust credible set and the optimal Bayes robust point estimator of the failure rate X are discussed using the r- posterior expected loss under the squared error loss as the criterion.更多还原