共因失效系统动态可靠性模型

考虑共因失效相关性，在系统层运用应力-强度干涉模型建立了共因失效系统可靠性模型。在研究系统可靠性模型的基础上，建立了系统强度的累积分布函数和概率密度函数。采用泊松随机过程来描述载荷的作用过程，运用概率微分方程和全概率公式建立了强度随时间退化时的串联系统、并联系统以及k/n系统动态可靠性模型。以强度退化服从指数退化规律为例，研究了串联系统、并联系统以及k/n系统的可靠度和失效率随时间的变化规律。研究表明:系统的可靠度随时间逐渐降低，k/n系统的可靠度介于串联系统和并联系统之间；系统的失效率具有“浴盆”曲线的特征。

Time-dependent Reliability Model of System with Common Cause Failure

Common cause failure as an important mode of dependent failure was considered and the reliability models of systems with common cause failure were built with the stress--strength interfer- ence model in system-level directly. Based on the analysis of models proposed, the cumulative distribution functions and probability density functions of strength of systems were derived respectively. The process of random load action was described with the Poisson stochastic process and the time--dependent reliability models of series system, parallel system and k/n system were developed with the probability differential equation and total probability formula when strength degenerated as time. Taking the degeneration of strength following the exponential rule as an example, the relationships between the reliability and failure rate of system and time were studied. The result shows that the reliability of system decreases gradually as time, the reliability of k/n system is between that of series system and parallel system, and the failure rate of system has the feature of bathtub curve.