# A Performance Prediction Method Utilizing Time-Dependent Subsystem Transfers between Family Systems
## 2 Problem Statement
### Traditional Performance Prediction  
Common traditional methods for reliability analysis include statistical approaches such as fault trees, Bayesian networks [41; 42], evidence theory, accelerated degradation rate models [43], and the utilization of Weibull and exponential distributions [44]. These methodologies have been extensively employed in assessing the reliability of diverse projects.  
[PERSON] et al. proposed an enhanced methodology for reliability analysis based on Bayesian networks with fuzzy multi-states, which is employed to evaluate the reliability and growth of complex redundant systems [45]. A Bayesian network, represented as a directed acyclic graph, serves as a graphical model that utilizes probability reasoning. Each node variable represents an information element, while the directed edges between nodes depict causal relationships among these elements. Conditional probability is utilized to quantify the degree of influence between each information element. Nodes and directed edges constitute the fundamental framework of a Bayesian network [46].  
The performance of evidence theory in reliability analysis was summarized by [PERSON] and [PERSON] using a simple algebraic function [47]. [PERSON] et al. developed a novel program for projecting the reliability gradient through the plausibility measure and belief measure in evidence theory, without necessitating any additional information [48].  
[PERSON] and [PERSON] introduced an expectation-maximization algorithm for modeling the failure data of systems with different failure models using limited Weibull mixture distributions, even in cases where the probability function is not explicitly known [49]. The mixed Weibull distribution model comprises weighted combinations of single Weibull distributions, offering a strong applicability and providing accurate fitting effects for various complex probability density curves. Different combinations of model parameters can capture diverse features of the fitted curve shape [50]. The Weibull distribution is widely employed as a life distribution model in reliability engineering, effectively describing changes throughout the entire lifecycle of mechanical and electronic devices [51].  
[PERSON] et al. conducted an analysis on the impact mechanism of coating thickness on the storage reliability of electrical connector contacts and investigated the storage stress as well as the corresponding contact failure mechanism under a specific storage profile. They established a degradation model for electrical connector contact performance, considering coating thickness under temperature stress, based on the Wiener process, which effectively quantifies the degree of influence that the coating thickness has on contact performance degradation [52]. In their study, [PERSON] and [PERSON] developed a novel extended accelerated degradation testing (ADT) model that incorporates stress to prevent significant prediction errors in contrast to constant-stress normal experiments [53].  
However, these methods are predominantly reliant on statistical data obtained from samples, necessitating extensive long-term reliability testing and the accumulation of a substantial amount of fault data. This can be challenging to achieve for complex systems.