Wiener过程性能退化产品可靠性评估新Bayes方法

A New Bayesian Method for Reliability Assessment of Products with Wiener Process Degradation

摘要:

针对Wiener过程性能退化产品的可靠性评估问题，通过分析先验分布和损失函数两个因素，提出一种新的Bayes方法.假定Wiener过程参数服从共轭先验分布，对求解参数的后验分布进行理论分析；基于平方损失、绝对损失、0 1损失3种损失函数，分别求得Bayes估计结果；对航空发动机可靠性评估进行了实例分析.相对于已有方法，该方法在求解参数的后验分布时具有更广泛的适用性，并且运算过程更简单.对于民航发动机可靠性评估这一特定应用，3种损失函数中选取绝对损失函数时参数估计的拟合程度最优.

关键词:Wiener过程性能退化模型; 可靠性评估; Bayes估计; 共轭先验分布; 损失函数

Abstract:

For the reliability assessment of products with Wiener process degradation, a new method of Bayesian estimation was proposed by analyzing two factors—prior distributions and loss functions. First, the posterior distribution of the parameters was theoretically derived with the assumption that the parameters of Wiener process follow the conjugate prior distribution. Then the Bayesian estimation results were calculated based on the quadratic loss function, absolute loss function and 0 1 loss function respectively. Finally, the reliability assessment of aeroengines was analyzed as a practical example. It is shown that this new method has a wider range of application, and its calculation process is simpler compared to existing methods. Moreover, for the reliability assessment of aeroengines, the parameter estimation based on the absolute loss function has the best fitting of these three loss functions.

Key words:Wiener process performance degradation model; reliability assessment; Bayesian estimation; conjugate prior distribution; loss function