## 1 Introduction
[PERSON], [PERSON], [PERSON] and [PERSON] derived the expressions for the mean and variance of the intrinsic frequency of an elastic linkage mechanism with random physical and geometrical parameters by using the generalized random factor method [17]. In addition, models for the mean, variance and coefficient of variation of the mean square values of the displacement and velocity response of the mechanism under random excitation were obtained by the algebraic synthesis method. Then, the mean and variance of the dynamic reliability of the system were obtained by means of the Poisson process theory. In addition to the movement accuracy of the mechanism, fatigue is an important failure mode in the reliability evaluation of mechanisms. Since mechanisms always contain malfunctions and perform cyclic work, the mechanism components are subjected to the repeated action of dynamic additional stresses, which causes fatigue damage of components and systems. In practical engineering, important industrial mechanisms such as robots need to undergo rigorous dynamic stress tests and fatigue experiments before leaving their factories. Some publications have analyzed the fatigue life of mechanism components, providing a theoretical basis for the fatigue reliability analysis of mechanisms [18; 19]. At present, there are fewer models for time-varying reliability analysis of mechanisms under the fatigue failure mode considering multiple failure factors of mechanisms. The main difference between the time-varying reliability models of the mechanisms based on stress analysis and the time-varying reliability models based on motion accuracy analysis is that the accuracy reliability models focus on the possible failures of the mechanisms at each position. However, it may cause large errors to use this method to analyze the reliability of the mechanism considering the influences of fatigue and dynamic stress. As shown in Figure 1, if the stress at each moment is calculated and interfered with the strength, the reliability of the system without failure at each moment is obtained. However, practical engineering requirements as well as the definition of system reliability state that reliability is the ability of a system not to fail within a specified time period. This requires the attention to the cumulative effect of damage caused by stress. In addition, organizations often have multiple failure factors that affect each other and accelerate the fatigue failure of the system. These failure factors will degrade due to different degradation mechanisms. For example, mechanism clearances will expand due to constant wear. Manufacturing defects may cause the local stiffness of a member to weaken and degrade due to repeated loads. The uncertainty of random operating loads increases the impact of multi-failure degradation factors on system reliability. Therefore, it is necessary to establish time-varying reliability models of the mechanisms with multi-failure factors under fatigue failure mode and analyze the dynamic effects of these failure factors on the time-varying reliability of the mechanism under different degradation states. Existing literature on the reliability of motion mechanisms mostly focuses on the study of reliability evaluation methods with accuracy as the performance index. There are few analyses on time-varying reliability analysis of mechanisms considering clearance, local stiffness variation and strength degradation of mechanisms. To address the above problems, the crank slider is taken as the research object in this paper and time-varying reliability models of multi-failure mechanism under fatigue failure mode are developed considering the joint influence of clearance, local stiffness weakening, strength degradation and random load, which can be used to analyze the dynamic influence of failure factors on the time-varying reliability of the mechanism under different degradation states. The article is organized as follows: in Section 2, the dynamic response analysis of the mechanism with failure factors is carried out.