# Acceleration of Service Life Testing by Using Weibull Distribution on Fiber Optical Connectors
## 3 Validation of the Procedure
### Acceleration Coefficients Estimation  
To estimate the acceleration factors for the evaluation, a model that represents lifetime use and stress, and a test plan, are required [17; 29]. For this paper, in which the stress was applied by the induced vibration, the reliability target was \(R(t)\) = 0.97 with a confidence level \(C\) = 0.90. The test required 15 samples, the time of the vibration applied was 2 h per axis (6 h total), and the PSD generated 2.306 Grms to represent the stress level of the vibration, which was calculated by Equation (22) [9]. \[A_{i}=10 log(2)\frac{PSD_{i}}{10\log(2)+m}\left[f_{i}-f_{i-1}\left(\frac{f_{i-1 }}{f_{i}}\right)^{m/10\log(2)}\right] \tag{22}\]  
where \(A_{i}\) is the area of the \(th\) row, \(PSD_{i}\) is the amplitude and \(f_{i}\) is the frequency of the \(i\)th row of the vibration profile applied, while \(f_{i-1}\) is the frequency of the (th \(-\) 1) row of the testing profile, and \(m\) is the slope given as follows [9]:  
\[m=\left.dB\right/Octaws \tag{23}\]  
and  
\[dB=10 log\left(PSD_{i}\right/PSD_{i-1}\right) \tag{24}\]  
\[Octavas=\frac{log\left(f_{i}\right/f_{i-1}\right)}{\log(2)} \tag{25}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Failure Times in Vibration Service Life Test**} \\ \hline \hline \multirow{2}{*}{**Sample ID**} & \multirow{2}{*}{**Failure Time (h)**} & **Insertion Loss Requirement** & **Insertion Loss Result** \\  & & **(dB)** & **(dB)** \\ \hline
1 & 4.670 & 0.400 & 0.501 \\
2 & 5.000 & 0.400 & 0.576 \\
3 & 5.500 & 0.400 & 0.485 \\
4 & 5.830 & 0.400 & 0.566 \\
5 & 12.289 & 0.400 & 0.464 \\
6 & 13.861 & 0.400 & 0.561 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vibration test insertion loss results. Figure 5: Vibration test insertion loss results with wavelengths (**a**) at 1310 nm; (**b**) at 1550 nm. \[Grms=\sqrt{\sum A} \tag{26}\]  
Table 2 shows the features of the vibration profile and its results. The next step corresponds to the [PERSON] probabilistic analysis, with the shape factor \(\beta=2.500\) and fatigue constant \(m=4\)[26]. Here, because the testing of 15 samples was not desirable, it was reduced to 6. The increased over-stress factor is given by Equation (27) [26]. \[Accelerated\ Factor=\left\{\frac{ln[1-c]}{n_{reduced}\times\ln[R(t)]}\right\}^{1/ \beta} \tag{27}\]  
where using the known values, we have  
\[Accelerated\ Factor=\left\{\frac{ln[1-0.90]}{6\times\ln[0.97]}\right\}^{1/ 2}=2.755\]  
Due to the reduced sample size, the time for testing increased, and was calculated as per Equation (28). \[Time_{new}=Time_{old}\times\left\{\frac{ln[1-c]}{n_{reduced}\times\ln[R(t)]} \right\}^{1/\beta} \tag{28}\]  
After replacing the known values, the new time for testing was  
\[Time_{new}=2\times\left\{\frac{ln[1-0.90]}{6\times\ln[0.97]}\right\}^{1/2}=5. 510\]  
Then, the vibration stress level (Grms) required increasing to reduce the test time to a desired time, as given by Equation (29) [26], and using the known values, the Grms accelerated was calculated as  
\[Grms_{accel}=Grms_{normal}\times\left[\sqrt[n]{Time_{new}}\sqrt[n]{Time_{old }}\right] \tag{29}\]  
\[Grms_{accel}=2.306\times\left[\sqrt[4]{5.510}\sqrt[4]{2}\right]=2.971\]  
Finally, the adjustment factor required to accelerate the vibration profile given was applied as in Equation (30):  
\[Adjusment\ Factor=\left[\frac{Grms_{accel}}{Grms_{normal}}\right]^{2} \tag{30}\]  
Figure 5:0  
The new accelerated vibration profile used for testing, including the adjustment factor, is shown in Figure 5:1 This profile is applied in the next section.