## 2 Theoretical Background  
### Step-Down Stress Accelerated Degradation Test  
The SDSADT is a common reliability test method used to evaluate the performance degradation of products under various stress conditions. The advantage of this method lies in its ability to obtain the reliability information of products under actual storage conditions within a shorter time, and to assist in identifying the potential failure modes and failure mechanisms of the products [22]. There are \(k\) accelerating stress levels \(S_{i}(i=1,2,\ldots,k)\), and \(S_{k}>S_{k-1}>\cdots>S_{1}>S_{0}\). In the SDSADT, \(S_{k}\) is assumed to be the initial stress level and \(S_{0}\) is the normal stress level. \(m_{i}\) is the number of detections at the stress level \(S_{i}\). Usually, the number of stress levels \(k\) should not be less than three. At the beginning of the test, the samples are subjected to the ADT under stress level \(S_{k}\), during which the samples are taken out for \(m_{k}\) performance tests. After a time \(t_{1}\), the stress level is reduced to \(S_{k-1}\), and the samples are then subjected to the ADT under stress level \(S_{k-1}\), during which the samples are taken out for \(m_{k-1}\) performance tests. The stress level is sequentially reduced until a certain termination time is reached. The variation trend of stress level over time in the SDSADT is shown in Figure 1.  
The storage life of products is mainly influenced by temperature and humidity. However, during storage, measures such as sealed packaging are often used to eliminate the impact of humidity on storage life. Therefore, this article employs a constant-humidity step-down temperature stress ADT. The Arrhenius model is commonly used when the temperature serves as the accelerating stress. The Arrhenius model describes the relationship between temperature stress and degradation paths. This actually reflects the fundamental idea of the Boltzmann distribution, which is the relationship between the probability of each state in the system and the energy and temperature. Therefore, the Arrhenius model can be seen as an application of the Boltzmann distribution under specific conditions. Based on the degradation characteristics of product performance parameters, the model is defined as follows [23]:  
\[h(S)=\zeta_{0}\cdot e^{-\frac{K}{K}} \tag{1}\]where \(\xi_{0}\) is the constant, determined by the product geometry and testing method. \(E\) is the activation energy, which is related to the material. \(K\) is the Boltzmann constant, with a value of \(8.6\times 10^{-5}\) eV/\({}^{\circ}\)C. \(S\) is the temperature stress level in Kelvin. The exponential term \(e^{-\frac{E}{K\Sigma}}\) in Formula (1) can be regarded as the Boltzmann factor, which represents the probability that the system is in a high energy state (i.e., needs to overcome activation energy \(E\)) at a given temperature \(S\).  
Accelerated stress levels can be standardized as follows:  
\[x_{i}=\frac{1/S_{0}-1/S_{i}}{1/S_{0}-1/S_{k}} \tag{2}\]  
It can be seen from (2) that \(x_{0}=0\), \(x_{k}=1\), and \(0<x_{i}\leq 1\)\((i=1,2,\dots,k)\). Then, Formula (1) can be changed to the following:  
\[h(x)=\exp(\alpha_{0}+\alpha_{1}x) \tag{3}\]  
where \(\alpha_{0}=\ln\xi_{0}-\frac{E}{K\xi_{0}}=\ln\xi_{0}-\frac{\omega}{\xi_{0}}\) and \(\alpha_{1}=\frac{E}{K}(1/S_{0}-1/S_{k})=\omega(1/S_{0}-1/S_{k})\). According to Formula (3), \(h(x)\) is the monotone increasing function of stress level \(x\). The higher the stress level, the more obvious the product degradation path. Taking \(y_{1}=h(x_{1})\) and \(y_{2}=h(x_{2})\), the geometric mean of \(y_{1}\) and \(y_{2}\) will be obtained at the arithmetic mean point of \(x_{1}\) and \(x_{2}\).