# Reliability Analysis of Vehicle Braking System Based on Hyperellipsoidal Dynamic Bayesian Network
## 5 Conclusions  
In this study, a framework for evaluating the dynamic reliability of a braking system is proposed by integrating super ellipsoid modeling, dynamic Bayesian network, and fuzzy theory. The following important conclusions can be drawn from the comprehensive analysis of brake system reliability:  
(1) This study proposes a dynamic reliability assessment method for brake systems that combines hyperellipsoid modeling, dynamic Bayesian networks, and fuzzy theory. The core of this method is the innovative integration of hyperellipsoid modeling and dynamic \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Event Number**} & \multirow{2}{*}{**Bottom Event Probability Importance**} & \multirow{2}{*}{**Event Number**} & \multirow{2}{*}{**Bottom Event Critical Importance**} \\  & & **in Descending Order** & & **(in Descending Order)** \\ \hline x8 & Speed sensor & x8 & Speed sensor \\ x3 & Air compressor & x12 & Smart valve \\ x13 & Gateway valve & x13 & Gateway valve \\ x12 & Smart valve & x3 & Air compressor \\ x10 & Unit brake & x4 & Air compressor motor \\ x16 & Solenoid valve & x7 & Pressure sensor \\ x4 & Air compressor motor & x9 & Pressure switch \\ x6 & Dryer & x5 & Air compressor control unit \\ x14 & EPAC valve & x11 & Parking unit brake \\ x15 & Anti-skid valve & x17 & Safety valve \\ x18 & Pipeline & x14 & EPAC valve \\ x17 & Safety valve & x15 & Anti-skid valve \\ x7 & Pressure sensor & x10 & Unit brake \\ x5 & Air compressor control unit & x1 & Main cylinder \\ x9 & Pressure switch & x6 & Dryer \\ x1 & Main cylinder & x16 & Solenoid valve \\ x11 & Parking unit brake & x18 & Pipeline \\ x2 & Brake cylinder & x2 & Brake cylinder \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Importance ranking of critical components for brake system failure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Event Number**} & \multirow{2}{*}{**Component Name**} & \multicolumn{2}{c}{**Hyperellipsoid**} & \multicolumn{2}{c}{**Interval**} \\ \cline{3-5}  & & **Probabilistic** & **Critical** & **Probabilistic** & **Critical** \\  & & **Importance** & **Importance** & **Importance** & **Importance** \\ \hline x1 & Main cylinder & 0.01255 & 0.01041 & 0.01256 & 0.01041 \\ x2 & Brake cylinder & 0.00161 & 0.00166 & 0.00162 & 0.00167 \\ x3 & Air compressor & 0.08891 & 0.06768 & 0.08891 & 0.06768 \\ x4 & Air compressor motor & 0.06092 & 0.02412 & 0.06093 & 0.02413 \\ x5 & Air compressor control unit & 0.01641 & 0.01719 & 0.01642 & 0.01720 \\ x6 & Dryer & 0.05653 & 0.0827 & 0.05654 & 0.00827 \\ x7 & Pressure sensor & 0.01676 & 0.02185 & 0.01676 & 0.02185 \\ x8 & Speed sensor & 0.09295 & 0.07960 & 0.09295 & 0.07961 \\ x9 & Pressure switch & 0.01422 & 0.01732 & 0.01423 & 0.01733 \\ x10 & Unit brake & 0.07449 & 0.01082 & 0.07449 & 0.01082 \\ x11 & Parking unit brake & 0.01224 & 0.01710 & 0.01224 & 0.01711 \\ x12 & Smart valve & 0.07604 & 0.07387 & 0.07604 & 0.07388 \\ x13 & Gateway valve & 0.07805 & 0.07098 & 0.07805 & 0.07099 \\ x14 & EPAC valve & 0.04356 & 0.01328 & 0.04356 & 0.01328 \\ x15 & Anti-skid valve & 0.03868 & 0.01262 & 0.03869 & 0.01262 \\ x16 & Solenoid valve & 0.06869 & 0.00747 & 0.06869 & 0.00747 \\ x17 & Safety valve & 0.02556 & 0.01385 & 0.02556 & 0.01386 \\ x18 & Pipeline & 0.03676 & 0.00326 & 0.03676 & 0.00326 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Bottom event significance. Bayesian network, which is applied to the reliability analysis of the braking system. The method provides the following significant advantages:  
Restriction of the value range of the root node: By introducing the super ellipsoid model, the value range of the root node in the dynamic Bayesian network is effectively constrained, which solves the conservatism problem that may arise from the traditional fuzzy Bayesian network in data processing. Improvement of evaluation accuracy: The method not only expands the technical way of brake system reliability assessment, but also significantly improves the accuracy and practicality of the assessment results.