In this paper, a novel multistage reliability model is provided as systems are often divided into many stages according to system degradation characteristics. Multistage hard failure (caused by random shock) process (MHFP) and multistage soft failure (caused by random shock and continuous degradation) process (MSFP) are introduced to describe the competing failure processes, where either the MSFP or MHFP would break down the system. The shock processes impact the system in three ways: (1) fatal load shocks cause hard failure immediately in the hard failure process; (2) time shocks cause a hard failure threshold changing; (3) damage load shocks cause degradation level increasing in the soft failure process. In this paper, a density function dispersion method is carried out to address the multistage reliability model, and the effectiveness of the proposed models is demonstrated by reliability analysis with the one-stage model. Finally, the multistage model is applied to a case study, the degradation process is divided into three stages, and the hard failure threshold can be transmitted twice. The proposed model can be applied in other multistage situations, and the calculation method can satisfy the accuracy requirements.

中文翻译：

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受竞争失效过程影响的多级系统的可靠性建模

在本文中，由于系统通常根据系统退化特性被划分为多个阶段，因此提供了一种新颖的多阶段可靠性模型。引入多级硬失效（由随机冲击引起）过程（MHFP）和多级软失效（由随机冲击和持续退化引起）过程（MSFP）来描述竞争失效过程，其中 MSFP 或 MHFP 会破坏系统. 冲击过程以三种方式对系统产生影响：（1）致命的负载冲击在硬故障过程中立即引起硬故障；(2)时间冲击导致硬故障阈值变化；(3)损伤载荷冲击导致软失效过程中退化程度增加。本文采用密度函数离散方法来解决多级可靠性模型，并通过单阶段模型的可靠性分析证明了所提出模型的有效性。最后，将多阶段模型应用于一个案例研究，将退化过程分为三个阶段，硬故障阈值可以传递两次。该模型可应用于其他多级情况，计算方法满足精度要求。