## 3. Strategical Approach
### Degradation Path and Acceleration Model  
For estimating the reliability information, a specific statistical model is required. If lucky, there is prior reliability information for the statistical model of the product or the prototype. In many practical cases, however, the prior reliability information is not available. To address this limitation, in this study, a degradation path model based on the Wiener process was introduced (for details, see [PERSON] and [PERSON] [2]). The Wiener process is widely adopted for its mathematical tractability and simplicity. Based on these advantages, the Wiener degradation path model is recommended for estimating reliability information with no prior information. The Wiener degradation path model, \(W(t)\), with a drift, \(\eta\), and diffusion constant, \(\sigma^{2}\), has the following properties:  
1. \(W(0)=0\);
2. \(\{W(t)\}\,t\geq 0\) has stationary and independent increments;
3. For \(0\leq t_{1}<t_{2}\), the increment, \(\Delta W\) (=\(W(t_{2})-W(t_{1})\)), is normally distributed with the mean \(\eta(t_{2}-t_{1})\) and variance \(\sigma^{2}(t_{2}-t_{1})\). Let \(Y(t)\) be the degradation characteristic at time \(t\), and define \(y(t)=Y(t)-Y(0)\). In this research, \(y(t)\) is modeled as the degradation quantity from the Wiener degradation path, and it is assumed that the drift, \(\eta\), depends only on the current stress level. Based on the Wiener degradation path model and the assumption of the CE model, the different segments of the degradation increment in Figure 4b can be merged in the single degradation path shown in Figure 4c. To estimate the degradation quantity from the degradation path for the different stress levels, an acceleration model is required for calculating the mean degradation quantity. When dealing with a single variable and a constant- or step-stress loading scheme, acceleration models, such as the Arrhenius law, exponential law, and power law, can be standardized using a simple linear form. For example, [PERSON] et al. [9]  
Figure 4: Test period for each stress level under the step-stress loading method. and [PERSON] and [PERSON] [10] adopted temperature as a stress variable and analyzed ADT data based on the Arrhenius model. [PERSON] and [PERSON] [11] considered the power model in analyzing ADT data for fatigue crack. * Arrhenius model: \(\eta(s^{\prime})=\delta_{0}{}^{\prime}\exp(-\delta^{\prime}{}_{1}/s^{\prime})\);
* (Inverse) power model: \(\eta(s^{\prime})=\delta_{0}{}^{\prime}(s^{\prime})^{\delta^{\prime}{}_{1}}\);
* Exponential model: \(\eta(s^{\prime})=\delta_{0}{}^{\prime}\exp(\delta^{\prime}{}_{1}s^{\prime})\). To simplify the acceleration model without losing generality, the stress level is standardized as follows (e.g., see [PERSON] and [PERSON] [1]):  
\[s_{i} =\frac{1/s^{\prime}{}_{0}-1/s^{\prime}{}_{i}}{1/s^{\prime}{}_{0}-1/ s^{\prime}{}_{M}}\text{ for the Arrhenius model,}\] \[=\frac{\ln s^{\prime}{}_{i}-\ln s^{\prime}{}_{0}}{\ln s^{\prime}{} _{M}-\ln s^{\prime}{}_{0}}\text{ for the power model,}\] \[=\frac{s^{\prime}{}_{i}-s^{\prime}{}_{0}}{s^{\prime}{}_{M}-s^{ \prime}{}_{0}}\text{ for the exponential model}\]  
where \(s^{\prime}{}_{0}\) and \(s^{\prime}{}_{M}\) mean the normal use condition and the maximum stress level, respectively. Applying the above standardization results in the following: \(s_{0}=0\), \(s_{M}=1\), and \(0\leq s_{i}\leq 1\) for \(i=1\) and \(2\) for the two-stress case and \(i=1\), \(2\), and \(3\) for the three-stress case.