## 2 Materials and Methods
### Dynamic Bayesian Networks and Related Research  
Although there are many manners in which prognostics and overall system health can be assessed for complex systems, the remainder of this paper will focus on one potential modeling method: the dynamic Bayesian network (DBN). Bayesian networks, such as the ones illustrated in Figure 2, are directed acyclical graphs that convey causal relationships through directed arcs between their nodes of associated conditional probabilities [9]. DBNs have been increasingly used in reliability and system safety-related research, as they allow for causal-based inference calculations on hard-to-measure system states while providing a clear direction-based relationship within the structure of the model. The conditional probability tables and initial value distribution used in the networks are calculated from available data or determined through expert-based opinions. Critical to a DBN's construction is the assumption that future operational conditions are known or stable enough for reliable modeling; works by [PERSON] et al. [10] and [PERSON] et al. [11] have begun to consider necessary conditions for capturing these missing data.  
Risk-focused and reliability engineering studies have shown the versatility of these models with respect to system reliability and monitoring system health. Early research connected DBN formalisms to reliability block diagrams [12], dynamic fault trees [13], and Markov chain models [14]. As part of their extensive literature review on the use of Bayesian networks for fault diagnostics, [PERSON] et al. [15] found that more recent research used these fundamental reliability relationships to pursue specific areas of reliability engineering research, including process, structural, and manufacturing systems. [PERSON] et al. [16] used DBNs to determine a dynamic availability assessment of safety critical systems, while [PERSON] [17] found that DBNs could be used to make safety decisions for tunnel constructions. [PERSON] et al. [18] relied on hidden Markov models (HMMs) to monitor system functionality through DBNs. These researchers wanted to capture the dynamic qualities that would otherwise not be accessible to static models. In addition to the use of DBNs for system diagnostic purposes, there has been some research into whether this method could be used for prognostics as well. [PERSON] et al. [19] represented a small industrial system through DBNs to determine the expected prognostics of the system. [PERSON] et al. [20] proposed the use of DBNs to monitor fault diagnostics and loss-of-coolant accident progression prediction in a high-temperature gas-cooled reactor pebble-bed module (HTR-PM) reactor. In each of these instances, an emphasis was placed either on the system health prognostics or diagnostics of the system; there has been limited effort made to combine this information into a single model.  
DBNs are also used in modeling for risk management of systems. Initial research by [PERSON] and [PERSON] [21] found that DBNs could be applied to a safety monitoring system to improve its capabilities. [PERSON] [22, 23] has shown the applicability of DBNs in capturing performance assessments in fires in chemical plants. [PERSON] et al. [1] have used DBNs as part of a process for providing risk-informed diagnosis procedures. However, there has not been a significant push to merge risk-informed dynamic Bayesian models with the system health of a complex engineering system to generate insight into the current health of the system.