二元相关退化系统可靠性分析及剩余寿命预测

退化相关性和个体差异对二元退化系统可靠性有直接影响,针对该问题,在退化过程模型基础上,建立了相应的系统可靠度和剩余寿命预测模型。首先同时考虑个体退化过程和相关性差异,采用随机参数的Gamma过程和Copula函数建立系统二元相关退化模型,为提高模型适用性,随机参数采用非共轭先验分布假设。在此基础上,分析随机参数对系统可靠度影响,提出基于贝叶斯理论的剩余寿命预测方法。利用马尔可夫链蒙特卡罗(Markov Chain Monte Carlo, MCMC)方法对模型未知参数进行估计。案例分析结果说明了在此类系统可靠性估计时考虑个体差异的必要性,也验证了该剩余寿命预测方法的精确性。

Reliability analysis and residual life estimation of bivariate dependent degradation system

Degradation dependency and individual difference have a direct influence on the reliability of bivariate degradation system. To solve this problem, based on the degradation process model, the corresponding system reliability and residual life prediction models are developed. Firstly, considering the individual differences of the degradation process and dependency simultaneously, a bivariate dependent degradation model of the system is developed using the Gamma process and the Copula function with random parameters, and to improve the applicability of the model, the assumption of non-conjugate prior distribution is adopted for random parameters. On this basis, the influence of stochastic parameters on system reliability is analyzed, and a residual life prediction method based on the Bayesian theory is proposed. The unknown parameters of the model are estimated by Markov chain Monte Carlo (MCMC) method. The case analysis shows the necessity of considering individual differences in reliability estimation of such systems, and also verifies the accuracy of the residual life prediction method.