## 4 Case Study
### Distribution and the Curve of Reliability  
Usually, the expert experience can be used to specify or use historical data of similar products to solve the model parameter distribution. However, this makes it difficult to ensure the objectivity of the final evaluation results and is not applicable when facing different products. Therefore, we hope to effectively use the relevant manufacturing information of the product and transform it into the basis for solving the model parameters in this paper. First, based on the AEMR's design and manufacturing process data, an approximate calculation model of release time versus initial read force is constructed. \[\left\{ \begin{array}{l}P_{r}=f(\Delta\Theta)\\ F_{ini}=f^{\prime}(\Delta\Theta)\end{array} \right. \tag{17}\]  
where \(\Delta\Theta=\left\{\Delta\Theta_{1},\Delta\Theta_{2},\cdots,\Delta\Theta_{j}\right\}\) denotes the variation of \(j\) design or the manufacturing process data that determine \(P_{r}\) or \(F_{ini}\). Then, according to the range of parameter fluctuations allowed in the relay manufacturing process, random sampling is carried out to obtain \(j\) sets of \(\Delta\Theta\), and they are substituted into Equation (17) for calculation. It results in \(j\) sets of \(F_{ini}\) that can be used to determine the \(P_{r}(0)\) distribution parameters. Based on the \(j\) sets of \(\Delta\Theta\), further batch AEMR's virtual samples are generated, and its storage degradation simulation is carried out to obtain the data, as shown in Figure 6.  
Finally, the obtained data are used for UMLE to acquire the distribution of the model parameters. Table 1 shows the statistics of the manufacturing process data situation, and Table 2 shows the parameter distribution. Figure 5: The data of AEMR’s storage degradation. Figure 6: The simulation data of AEMR’s storage degradation. For products at the early stage of development, it is difficult to go with the method of obtaining data by conducting a large number of sample storage degradation tests, for reliability assessment, with the help of mathematical and statistical methods. However, this problem can be circumvented based on belief reliability theory, so in this paper, only five sets of AEMR failure data are used to solve the failure threshold distribution parameters by UML estimation. Table 3 shows the small sample failure data. The distribution result of the contact failure threshold of AEMR was obtained as: \(\omega\sim N(1718.2,104.8)\). After all the uncertainty distribution parameters of the degradation model parameters are obtained, the storage reliability curve of the batch of AEMRs can be solved according to the reliability function, and the curve in Figure 7 shows the reliability life \(t_{0.9}=691.6\) h, \(t_{0.8}=7896.1\) h. From the trend of the curve, it can be seen that the product's reliability decreases at the fastest rate in the early stage and gradually levels off in the middle and late stages, which also coincides with the law of stress relaxation. In order to further verify the effectiveness and accuracy of the method, the performance degradation modeling, based on the stochastic process, is carried out in this paper. The reliability evaluation is carried out using experimental (M1) and simulation (M2) data, respectively. The contrast of M1, M2, and M3 is shown in Figure 8. By comparison with M1, it can be seen that the error of curve M3 is smaller than that of M2. However, the trend of curve M3 decreases faster in the early stage, mainly because the degradation modeling only considers the factor of stress relaxation and ignores the influence of coupling with other influencing factors on the degradation process. The main reasons for the deviations in the results, based on the simulation data, may be errors in the approximate modeling process, the fact that the simulation was carried out with only a single consideration of