# Phased System Reliability Modeling and Assessment for Construction of Lunar Scientific Base
## 3 Reliability Assessment Method for Three Main Processes  
The phased reliability model proposed in Section 2 ensures that the reliability confidence limits for the three main processes are independent. However, each process (such as fixed-point delivery) is performed many times, and the reliability confidence limits of each fixed-point delivery may be correlated. This section gives the reliability assessment methods for the three main processes, taking the fixed-point delivery process as an example.  
Suppose \(m_{1}\) fixed-point delivery will be carried out during the LSB construction, and denote \(R_{A\ i}\) as the reliability of the \(i\)th fixed-point delivery, \(i=1,2,\ldots,m_{1}\). The individual fixed-point deliveries are independent and form a serial system. The reliability block diagram is shown in Figure 4.  
The reliability \(R_{A}\) of the overall fixed-point delivery can be expressed as  
\[R_{A}=\prod_{i=1}^{m_{1}}R_{Ai}\ \ \ \ \ i=1,2,\ldots,m_{1} \tag{1}\]  
In engineering practice, the true value of \(R_{Ai}\) is unknown. Indeed, its LCL with the confidence degree \(\gamma\) is required and evaluated through the corresponding reliability test, which satisfies  
\[P\big{(}R_{Ai}\geq R_{Ai,\gamma}\big{)}=\gamma\ \ \ \ \ i=1,2,\ldots,m_{1} \tag{2}\]  
Due to the risk-averse design, space engineering requires a high confidence degree indicator \(\gamma\) (i.e., a confidence degree of not less than 0.9). A confidence degree of 0.9 means that there is 90% certainty that the true value of the reliability is not less than the LCL of the reliability estimated from the test sample. Theoretically, the assessment results are safe and secure.  
Figure 4: The reliability block diagram of fixed-point delivery.  
Figure 3: A subtask reliability model for LSB construction.  
It is well known that the reliability of a series system is the product of the reliability of the individual subsystems. However, is the LCL of the series system reliability also the product of the LCL of the individual subsystem reliability? Moreover, how does one calculate the confidence degree for the LCL of the system reliability in this case? Inspired by the above problem, this section will discuss the LCL of the overall fixed-point delivery reliability \(R_{\rm A}=\prod_{i=1}^{m_{1}}R_{Ai}\) with the confidence degree \(\gamma\) in two cases: identical and different reliability. Before discussing, definitions of the relevant concepts are first given. According to interval estimation theory, it is known that confidence limits of reliability are statistically inferred from the test sample.  
1. If the reliability confidence limits of subtasks are inferred from the same test samples, it can be said that they have identical reliability; in other words, the reliability confidence limits are correlated.
2. If the reliability confidence limits of subtasks are inferred from different test samples, it can be said that they have different reliability; in other words, the reliability confidence limits are independent.
3. In either case, the reliability \(R_{Ai}\) of each fixed-point delivery is independent (random events are independent).