## 1 Introduction  
Reasonable electromechanical system maintenance plans are often made according to system reliability in order to reduce failures that cause production, personnel, and environmental losses [1; 2; 3]. Therefore, it is important to accurately grasp the changing law of system reliability [4; 5]. Traditional reliability theory often ignores working conditions (WCs), which are commonly assumed to have no influence or to always remain in a constant state [6; 7]. However, with increasing requirements for production efficiency, the lack of consideration of WCs in system reliability evaluation can cause unacceptable deviations [8; 9]. Therefore, the motivation of this paper is to study the system failure intensity (FI) in dynamic WCs accurately, which is an important indicator for repairable system reliability. Due to the increasing significance of WCs in reliability research, many new methods have been proposed by scholars. For example, [PERSON] et al. [10] used Markov chains to symbolize the conditions, so dynamic conditions could be described by aggregating different Markov chains, and good results were achieved. By using acceleration models, [PERSON] et al. [11] linked the system reliability to various environmental factors, which display characteristics such as variability, dependency, and randomness. [PERSON] [12] developeda two-stage model to assess the reliability of a degradation system in the dynamic environment. In addition, [PERSON] et al. [13] proposed a multi-component system reliability model based on the cumulative exposure principle, which transfers the equivalent working time to a monotone increasing stochastic time scale. This model was perfectly applied in an automobile braking system. At present, performance degradation and failure are the two perspectives from which to study the influence of WCs on equipment reliability. From the aspect of degradation, the state of equipment is reflected by monitoring changes in the performance state. The influence of WCs on the equipment is mainly reflected in the influence of performance degradation. Through the application of an intelligent algorithm, the influence of different WC factors on varying performance indicators can be achieved effectively. Regarding the statistical model, although these previous studies examined different fields and objects, their relationship models between WCs and system reliability can be roughly divided into physical models and statistical models. Physical models consider the effect of some specific stresses in WCs on product life from the perspective of failure mechanisms [14; 15]. Since various stresses are complexly coupled, it is difficult for physical models to deal with more complex situations [16]. On the other hand, statistical models discard in-depth research on system mechanisms while starting directly from the perspective of statistical data, so they are not restricted by the application objects [17]. Regarding statistical models, two models have been widely used; these are the accelerated model (AM) [18] and the proportional model (PM) [19]. The AM assumes that there is a linear relationship between failure time and WCs which creates the impact of WCs on systems over time. [PERSON] et al. [20] established the failure model of metal oxide-based surge arresters when exposed to harmonics. In [21], the AM was extended to the case where the scale parameter was not the parameter impacted by the stresses. [PERSON] et al. [22] used the advantage of generalized lambda distributions (GLD), which enhance the capabilities of the AM. [PERSON] et al. discussed the measurement error in the AM [23]. In the PM, the WCs' effects were treated as a covariate function. The differences between various WCs can be reflected in the multiplier effects. [PERSON] et al. [24] considered the effect of the environment on the mean deterioration rate as a covariate in the PM. [PERSON] et al. [25] adopted the PM to analyze the effects of aging and covariates on the outage process in power systems.