# A Performance Prediction Method Utilizing Time-Dependent Subsystem Transfers between Family Systems
## 2 Problem Statement  
### Complex Systems Engineering  
In practical applications, as one of the main research objects in reliability analysis engineering, the research and development of complex systems science also significantly affects the effectiveness and application of reliability analysis. The complexity of complex systems is mainly caused by factors such as intricate environments, human factors, and subsystem relationships. Therefore, describing the functioning of complex systems through establishing mathematical models becomes challenging, especially when dealing with various unknown parameters.  
Research conducted by scholars in the field of complex systems has revealed that these systems are typically composed of multiple interconnected and interdependent units, each possessing unique properties or characteristics not found in individual components. In essence, comprehending the constituent parts of a complex system does not equate to understanding the overall system, as it is more than just an amalgamation of its elements. The continuous evolution and enhancement of such systems is driven by their mutual interactions with various subsystems and their surrounding environment, rather than being determined solely by any single or pair of influencing factors. These interactions exert a high level of sensitivity on the system, whereby even minor changes between elements can result in entirely different outcomes [37].  
Therefore, the incorporation of complex systems science is crucial for comprehensively assessing research progress in reliability engineering. [PERSON]'s work distinguishes three key components based on complex systems science techniques, as follows: data analysis (including statistical analysis and data mining), model building and understanding, and measuring complexity itself [38]. [PERSON] and [PERSON] proposed a formalization method utilizing dynamic object-oriented Bayesian networks to evaluate system reliability [39]. Additionally, [PERSON] et al. combined relationships across time fragments to classify network segments with similar structures and parameters, thereby constructing a dynamic object-oriented Bayesian network [40].  
Based on current research, the field of complex system engineering encounters several challenges, as follows:  
1. The design and application of such complex systems primarily remain in the conceptual and developmental stages, lacking sufficient experiential knowledge to draw upon, consequently leading to numerous defects during initial testing and production phases.
2. In-depth investigation is required for data processing and data mining in system operation, as complex systems impose stringent requirements without readily available samples.  
Complex systems exhibit uncertain states with intricate and often variable operating environments, rendering disturbances influenced by environmental changes highly unpredictable.  
Currently, the advancement of information technology has led to the integration of numerous sensors in new complex systems, thereby establishing a robust data foundation for performance prediction.