## 3 Storage Degradation Belief Reliability Model for AEMR
### Analysis of the Storage Degradation Mechanism of Aerospace Relays  
During long-term storage, the internal reeds, coils, bobbins, enameled wires, and magnetic materials of AEMR can degrade to a certain degree, affecting their movement and contact characteristics. The relay will fail when the movement or contact characteristics are outside the allowable range. However, for the AEMR in storage, the leading cause of failure is the stress relaxation of the reeds, which reduces the reaction force and affects the reaction force characteristics, increasing the release time during operation and, finally, leading to contact failure.  
As the reed is sealed in the internal component of the relay, it is not easy to open and test the stress relaxation state of the reed in the actual storage environment. Therefore, this paper obtains the relationship between the two by conducting finite element simulation to verify the effect of reed reaction force variation on release time. The result is shown in Figure 2.  
Figure 1: AEMR’s belief reliability modeling framework.  
Figure 2: Relationship between initial force and release time.  
The simulation results show an approximately linear relationship between the external performance parameter (release time \(P_{r}\)) and the underlying performance parameter (reed initial force \(F_{ini}\)) within a certain range of reed reaction force reduction. Therefore, this paper uses Equation (4) to express the relationship between the two:  
\[P_{r}=k\cdot F_{ini}+c \tag{4}\]  
where \(k,c\) are model coefficients related to the design and manufacturing process, which characterize the variability between individual relays of the same batch.  
From the above analysis, it is clear that the stress relaxation occurring in the internal reed during the storage period of the AEMR is the fundamental reason for the reduction in the reaction force. Therefore, in this paper, the initial force is used as the characterization parameter of the mechanical reaction force, and the Larson-Miller coefficient is used to describe the storage degradation process of the reed under the joint action of temperature stress (Kelvin) and time (hours), and the corresponding physical model of failure is obtained as shown:  
\[\begin{array}{rl}\frac{F_{ini}(t,T)}{F_{ini}(0)}&=a\cdot\Theta+b\\ &=a\cdot T(\ln t+C)+b\end{array} \tag{5}\]  
where \(F_{ini}(t,T)\) is the reed initial force value at temperature stress \(T\)  
Larger-the-better performance parameter: the product fails when and only when \(P\leq P_{th}\).  
Nominal-the-type performance parameter: the product fails when and only when \(P\geq P_{th.L}\) or \(P\leq P_{th.U}\).  
Therefore, the margin equation, constructed as follows, is shown:  
\[G(P,P_{th})=\left\{\begin{array}{l}\frac{P_{th}-P}{P_{th}},smaller\text{ {the better}}\\ \frac{P_{-P_{th}}}{P_{th}},larger\text{ {the better}}\\ \min\left(\frac{P_{th,U}-P}{P_{th,U}},\frac{P-P_{th,L}}{P_{th,L}}\right), nominal\text{ {the better}}\end{array}\right. \tag{8}\]  
Based on the failure mechanism of a relay during storage, it is generally believed that a contact failure will occur when the stress relaxation-induced release time increases to a certain threshold value. Therefore, the growth of the release time to a certain threshold value can be used as a judgment condition for relay storage failure, and the release time \(P_{r}(t)\) is used as the expected small performance parameter to construct the margin equation, where \(\omega\) is the failure threshold value.  
\[G=\frac{\omega-P_{r}(t)}{\omega} \tag{9}\]  
It is considered reliable when the margin \(G\geq 0\), so the reliability equation can be established as:  
\[\begin{array}{lcl}R(t)&=&M(\frac{P_{r}(t)-\omega}{\omega}\leq 0)\\ &=&M(\frac{[P_{r}(0)-c]\cdot[a^{\prime}\cdot\ln(t+1)+b)]+c-\omega}{\omega}\leq 0 )\\ &=&M([P_{r}(0)-c]\cdot[a^{\prime}\cdot\ln(t+1)+b)]+c-\omega\leq 0)\end{array} \tag{10}\]