# Device Reliability Analysis of NNBI Beam Source System Based on Fault Tree
## 5 Fault Tree Analysis
### Failure Rate Analysis of Plasma Expansion Chamber  
During the entire test cycle, the plasma expansion chamber failed a total of 27 times, and the specific failures are as follows:  
1. The Cs injection system has experienced a total of 17 failures, including 1 upper pipeline valve failure, 2 upper pipeline heating wire failures, 3 upper pipeline thermocouple failures, 2 lower pipeline heating wire failures, 1 lower pipeline valve failure, 3 lower pipeline thermocouple failures, 1 Cs Pressure regulation display screen malfunction, 2 Cs control cabinet failures, 1 Cs pipeline contamination incident, and 1 Cs nozzle failure. The total failure rate of the Cs injection system is \(\lambda_{\rm T}\) = 17/(166 \(\times\) 24) = 4.28 \(\times\) 10\({}^{-3}\). 2. The bias plate has experienced a total of 7 failures, including 5 power supply failures, 1 water cooling pipe (backplane water inlet pipe of the expansion chamber (ECBP2)) leakage incident, and 1 thermal deposition polishing/cleaning event. The overall failure rate of the bias plate is \(\lambda_{\rm T}\) = 7/(166 \(\times\) 24) = 1.76 \(\times\) 10\({}^{-3}\). 3. The magnetic filter in the filtering magnetic field has failed 3 times, resulting in a failure rate of \(\lambda_{\rm T}\) = 3/(166 \(\times\) 24) = 7.53 \(\times\) 10\({}^{-4}\). The failure rates of each subsystem in the plasma expansion chamber are shown in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Failed Component** & **Fault Bottom Event** & **Component** & **Total Failure** \\  & & **Failure Rates** & **Rate** \\ \hline \multirow{6}{*}{Plasma Electrode Failure} & The surface flatness is not up to standard & 2.51 \(\times\) 10\({}^{-4}\) & \\  & Electrode Endplate Blockage Fault & 2.51 \(\times\) 10\({}^{-4}\) & \\  & many impurities deposited on the electrode. & 2.51 \(\times\) 10\({}^{-4}\) & \\  & PG electrode water pipe is leaking & 7.53 \(\times\) 10\({}^{-4}\) & \\  & Electrode Over-Deposition Polishing & 5.02 \(\times\) 10\({}^{-4}\) & \\ \hline The common cause basic event & PG and EG short circuit & 5.02 \(\times\) 10\({}^{-4}\) & 5.02 \(\times\) 10\({}^{-4}\) \\ \hline \multirow{6}{*}{Extraction Electrode Failure} & Electrode Cooling Water System Failure & 1.26 \(\times\) 10\({}^{-3}\) & \\  & EG excessive impurity deposition & 1 \(\times\) 10\({}^{-3}\) & \\  & Support cover is insufficiently flat & 5.02 \(\times\) 10\({}^{-4}\) & \\  & Replace the power supply chip & 2.5 \(\times\) 10\({}^{-4}\) & \\ \hline \multirow{3}{*}{Accelerated electrode failure} & AG water pipe leaked & 2.51 \(\times\) 10\({}^{-4}\) & \\  & AG excessive impurity deposition & 2.51 \(\times\) 10\({}^{-4}\) & \\  & AG Thermal deposition grinding and cleaning & 5.02 \(\times\) 10\({}^{-4}\) & \\ \hline \multirow{3}{*}{Ground electrode fault} & excessive impurity deposition & 2.51 \(\times\) 10\({}^{-4}\) & \\  & GG water pipe leaked & 2.51 \(\times\) 10\({}^{-4}\) & \\ \cline{1-1}  & GG Thermal deposition grinding and cleaning & 5.02 \(\times\) 10\({}^{-4}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: NNBI Negative Ion Accelerator Fault Events and Fault Rates (unit: 1/h).