## 2 Basic Theories
### Dynamic Bayesian Network
The system state satisfies the discretization according to the above assumptions and after dividing the time segments by a dynamic Bayesian network, the process complies with the Markov assumption and the chi-squaredness assumption; (1) The state of the current moment is only related to the state of the previous moment; (2) For any moment \(t\), the state transfer probability \(P(X_{t}|X_{t-1})\) is constant [35]. The number of state spaces is limited to three states. Thus, system state modeling can be performed by using Markov chains in dynamic Bayesian networks [14]. According to the assumption that the node failure state obeys the exponential distribution of failure rate \(\lambda\), the corresponding transfer relationship table of the vehicle operation process without and with maintenance state can be obtained [1], as shown in Table 2 below. Planned maintenance is not included in the Consider maintenance. The logical relations in the table are the transfer probability calculation formulas for the transfer of each state of the node under t moments to each state under (t + \(\Delta\)t) moments. T-S polymorphic fault trees transform the structure learning in DBN, and the specific rules are shown in Figure 2. The next-level input events in the T-S gate are similar to the parents in the conditional probability table of the Bayesian network. The upper-level output events are similar to the children. In contrast, the T-S gate rule satisfies the conditional probability and independence, so the T-S gate rule is used to assign the conditional probability table to the corresponding nodes in the Bayesian network. The dynamic changes of nodes in T-S gates in T-S multistate fault trees can be directly added with directed edges between time segments to complete the expansion from moment \(t\) to (t + \(\Delta\)t) moment, as shown in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{No Consideration for Maintenance} \\ \hline \(t+\Delta t\) & \(t\) & 0 & 0.5 & 1 \\ \hline \(0\) & \(e^{-(\lambda_{1}+\lambda_{2})\Delta t}\) & 0 & 0 \\ \(0.5\) & \(\frac{\lambda_{1}}{\lambda_{1}+\lambda_{2}}(1-e^{-(\lambda_{1}+\lambda_{2}) \Delta t})\) & \(e^{-\lambda_{3}\Delta t}\) & 0 \\ \(1\) & \(\frac{\lambda_{3}}{\lambda_{1}+\lambda_{2}}(1-e^{-(\lambda_{1}+\lambda_{2}) \Delta t})\) & \(1-e^{-\lambda_{3}\Delta t}\) & 1 \\ \hline \(t+\Delta t\) & \(t\) & 0 & 0.5 & 1 \\ \hline \(0\) & \(e^{-(\lambda_{1}+\lambda_{2})\Delta t}\) & 0 & \(1-e^{-u\Delta t}\) \\ \(0.5\) & \(\frac{\lambda_{1}}{\lambda_{1}+\lambda_{2}}(1-e^{-(\lambda_{1}+\lambda_{2}) \Delta t})\) & \(e^{-\lambda_{3}\Delta t}\) & 0 \\ \(1\) & \(\frac{\lambda_{2}}{\lambda_{1}+\lambda_{2}}(1-e^{-(\lambda_{1}+\lambda_{2}) \Delta t})\) & \(1-e^{-\lambda_{3}\Delta t}\) & \(e^{-u\Delta t}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Root node state transfer relationship table. Figure 3: Root node multistate transition diagram. The conditional probability table (CPT) in DBN can express the correlation between devices and the impact of different failure states of devices on system reliability. The CPT of DBN in this method is converted from the T-S gate rule, and the probability of failure of the output event can be calculated by the probability of failure of the T-S gate input event, which corresponds to the CPT in DBN.