This paper studies the reliability problem for systems subject to two types of dependent competing failure processes, that is, soft failure and hard failure processes. A soft failure happens when the total degradation of the system exceeds a given critical level, while a hard failure occurs when the accumulative shock load caused by shocks surpasses the hard failure threshold. These two failure processes are mutually dependent due to the fact that external shocks will bring sudden increments in the degradation of the system, and the total amount of degradation will decrease the hard failure threshold of the system. The system fails whenever either of these two failure modes happens. Assuming that the arrival of shocks follows a Poisson process, the reliability function of the system under cumulative shock model is derived by using some analytical techniques. Some important reliability indices, including the mean lifetime of the system, the expected number of shocks until system failure, the probabilities of soft and hard failures, are calculated explicitly. Moreover, a special case that the hard failure process and soft failure process are mutually independent is also discussed. Monte Carlo method is employed to calculate the multiple integrals existing in the expressions of reliability function and reliability indices. A numerical example of the Reinforced Concrete pier columns on sea bridge is presented to illustrate the proposed model.

本文研究了受两类相互依赖的竞争故障过程（即软故障和硬故障过程）的系统的可靠性问题。当系统的总降级超过给定的临界水平时，将发生软故障，而当由冲击引起的累积冲击负荷超过硬故障阈值时，将发生硬故障。这两个故障过程是相互依赖的，这是由于以下事实：外部冲击将使系统的性能突然增加，并且总的降低量将降低系统的硬故障阈值。每当这两种故障模式之一发生时，系统都会发生故障。假设冲击的到来遵循泊松过程，利用一些解析技术推导了系统在累积冲击模型下的可靠性函数。明确计算了一些重要的可靠性指标，包括系统的平均寿命，预期的直到系统故障的电击次数，软故障和硬故障的概率。此外，还讨论了硬故障过程和软故障过程相互独立的特殊情况。采用蒙特卡罗方法计算可靠性函数和可靠性指标的表达式中存在的多个积分。给出了海桥上钢筋混凝土墩柱的数值实例，以说明所提出的模型。软故障和硬故障的概率是明确计算的。此外，还讨论了硬故障过程和软故障过程相互独立的特殊情况。采用蒙特卡罗方法计算可靠性函数和可靠性指标的表达式中存在的多个积分。给出了海桥上钢筋混凝土墩柱的数值实例，以说明所提出的模型。软故障和硬故障的概率是明确计算的。此外，还讨论了硬故障过程和软故障过程相互独立的特殊情况。采用蒙特卡罗方法计算可靠性函数和可靠性指标的表达式中存在的多个积分。给出了海桥钢筋混凝土墩柱的数值实例，以说明所提出的模型。