## 4 FMEA Analysis of Three-Engine Pouring Control System
### Fault Tree Analysis of Control Circuit System
#### 5.2.2 Quantitative Analysis  
The failure rate of each component is calculated based on the GJB/Z299D Electronic Equipment Reliability Prediction Manual, as shown in Table 2. The parameters involved are the basic failure rate \(\lambda_{b}\), the environmental coefficient \(\pi_{E}\), the contact form factor \(\pi_{C_{1}}\), the contact load factor \(\pi_{L}\), the mass coefficient \(\pi_{Q}\), the rate of action factor \(\pi_{CYC}\), the applied structural coefficient \(\pi_{A}\), the utilization factor \(\pi_{U}\), and the rated voltage coefficient \(\pi_{V}\).  
Figure 8: The fault tree model of the three-engine pouring control system.  
By consulting the Electronic Equipment Reliability Prediction Manual, the working failure rate of the time relay can be calculated as follows:  
\[\lambda_{p}=\lambda_{b}\pi_{E}\pi_{Q}\pi_{C_{1}}\pi_{CYC}\pi_{A} \tag{1}\]  
where the basic failure rate is 0.094, the environmental coefficient is 1, the mass coefficient is 0.3, the number of contacts is 2, and the contact form factor is 1.7; the action rate coefficient and applied structure coefficient are taken as 0.1 and 10, respectively.  
The calculated value of the working failure rate of the time relay is 0.096 \(\times\) 10\({}^{-6}\).  
The working failure rate of the proximity switch  
According to the relevant parameters of similar proximity switches, the failure rate of the proximity switches is taken as:  
\[\lambda_{pf}=0.431\times 10^{-6} \tag{3}\]  
The working failure rate of the knob switch  
The working failure rate of the switch can be calculated as:  
\[\lambda_{p}=(\lambda_{b1}+\lambda_{b2})+\pi_{E}\pi_{Q}\pi_{L}\pi_{CYC} \tag{2}\]  
where the basic failure rate of the knob-type switch drive mechanism is 0.3, and the basic failure rate of the switch active contact is 0.14.  
The calculated value of the working failure rate of the available knob switch is 0.736 \(\times\) 10\({}^{-6}\).  
The working failure rate of the button switch  
The basic failure rate of the drive mechanism in the button switch is 0.28, and the values of parameters are the same as those of the knob switch.  
The calculated value of the working failure rate of the available button switch is 0.576 \(\times\) 10\({}^{-6}\).  
The working failure rate of the indicator light is calculated as follows:  
\[\lambda_{p}=\lambda_{b}\pi_{E}\pi_{U}\pi_{V} \tag{3}\]  
based on the Electronic Equipment Reliability Prediction Manual, the basic failure rate of indicator light is 0.34; the environmental coefficient is 1.0; the utilization factor is 0.1; the rated voltage is 24 V, and the corresponding rated voltage coefficient is 7.6. The calculated value of the working failure rate of the indicator light is 0.258 \(\times\) 10\({}^{-6}\).  
According to the working failure rate of the electro-acoustic device, the failure rate of the buzzer is determined as  
\[\lambda_{pf}=0.245\times 10^{-6}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Failure Rate** & **Name** & **Failure Rate** \\  & **(10\({}^{-6}\))** & **Name** & **(10\({}^{-6}\))** \\ \hline Time relay & 0.096 & proximity switch & 0.431 \\ Knob Switch & 0.736 & Main Switch & 0.576 \\ Indicator light & 0.258 & buzzer & 0.245 \\ Low-voltage DC power supply & 0.857 & Fuse & 0.150 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The failure rate of each component of the three-engine pouring control circuit system.  
Note that the work failure rate of the buzzer can represent the work failure rate of the bell.  
The working failure rate of low-voltage DC power supply  
The operating failure rate of the low-voltage DC power supply is determined as  
\[\lambda_{py}=0.857\times 10^{-6}\]  
The working failure rate of the fuse is given by  
\[\lambda_{pr}=0.150\times 10^{-6}\]