## 5 Engineering Application
### Preliminary Assessment of the IES Reliability  
During the design and development stage, the IES lacks test and operational data of the whole system and must rely on the life data of its key components to assess system reliability. Historical life data are available for electronic circuits and rotating devices. The 91 electronic circuits have accumulated a total flight time of approximately \(T_{1}\) = 395.10 years with no failures. Similarly, the past service life data of the 74 rotating devices, presented in Table 2, also show no failures. Figure 5: Reliability block diagram of IES. Given that the infrared detector is a newly designed product without available historical data, a constant stress accelerated life test was performed. Temperature served as the accelerating stress, and the noise factor was used as the performance index. A total of 127 specimens were tested across four selected temperature stress levels, with specimens at each level tested for 143 days. At the end of the test, none of the specimens failed. The test results are shown in Table 3, and the process of determining the acceleration factor is illustrated in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Sample Size** & **Flight Time** & \multirow{2}{*}{**No.**} & **Sample Size** & **Flight Time** & \multirow{2}{*}{**No.**} & **Sample Size** & **Flight Time** \\  & **Size** & **(Years)** & & & & **Size** & **(Years)** & \\ \hline
1 & 2 & 8.2 & 9 & 6 & 5.2 & 17 & 4 & 3.1 \\
2 & 2 & 8.1 & 10 & 2 & 4.8 & 18 & 1 & 2.7 \\
3 & 2 & 7.8 & 11 & 4 & 4.7 & 19 & 2 & 2.6 \\
4 & 4 & 6.8 & 12 & 4 & 3.9 & 20 & 9 & 2.5 \\
5 & 2 & 6.7 & 13 & 2 & 3.8 & 21 & 2 & 2.1 \\
6 & 4 & 6.5 & 14 & 2 & 3.6 & 22 & 8 & 1.8 \\
7 & 2 & 5.6 & 15 & 2 & 3.5 & 23 & 2 & 1.3 \\
8 & 2 & 5.5 & 16 & 2 & 3.4 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Historical flight data for rotating devices (no failures). Figure 6: Flowchart for determining the acceleration factor. Based on the total flight time of the electronic circuits, and the zero-failure data for the rotating device and infrared detector presented in Tables 2 and 3, the following is a preliminary assessment for the LCL of the IES reliability at a confidence level of \(\gamma=0.9\). First, it is necessary to determine the component lifetime distributions. Since failure time data are unavailable, verifying the lifetime distribution models through goodness-of-fit tests is difficult. Instead, the suitability of the modes must be analyzed in conjunction with the failure pattern and the model characteristics. Electronic circuits are mainly prone to random failures, and their life usually follows an exponential distribution. Rotating devices are susceptible to wear-type failures, making the Weibull distribution appropriate for modeling their life. [PERSON] (2018) conducted an accelerated life test study of infrared detectors based on the assumption that the life of optoelectronic products follows an exponential distribution. On this basis, the shape parameter values corresponding to the lifetime distributions are provided. Next, the GTT \(T_{i}\)\((i=1,2,3)\) of the three components is calculated using Equation (5). The results of the above analyses and calculations are summarized in Table 4.  
The lifespan requirement for the IES is 8 years (i.e., \(t\) = 8 years). According to Equation (7), it follows that  
\[\eta(8)=\min\left(\frac{T_{1}}{8},\frac{T_{2}}{81.5},\frac{T_{3}}{8}\right)= \frac{T_{2}}{81.5}=29.9 \tag{28}\]  
Using Equation (8), the LCL of the IES reliability at a confidence level of \(\gamma=0.9\) can be obtained. For comparison, the LM method is also performed. The results are summarized in Table 5.  
The preliminary assessment of the two methods concluded that the IES does not satisfy the reliability index requirement of 0.93. This is because, despite collecting a substantial number of component life data samples, all available data are zero failures, providing minimal informative content.