# A Predictive Reliability Model to Assess the Performance of Photovoltaic Systems
## 3 Results and Discussion
### Results of Factorial Design Experiments  
The Taguchi OA factorial design experiments showed the dependency of the responses on the factors and the significance of such a dependency. The software DOE++ provided the  
Figure 3: Efficiency of the PV system calculated over the 12 months for three orientations of the two regions. Figure 2: Array yield over the 12 months for three orientations of the two regions. results in different formats, from which we studied the significance of the factors based on their \(p\_values\) and the equations describing the dependency of the responses on the factors. The significance of each of the four factors (\(G_{eff}\), \(T_{A}\), \(V_{w}\), \(Y_{a}\)) and their combinations is given in percentages such that:  
\[significance\ =\ (1-p\_value)\ *\ 100\%\]  
The most significant factors and their levels of significance on the three responses (\(\eta\), \(PR\), \(E_{prod}\)) are presented in Tables 3 and 4 for near Cairo and near Riyadh, respectively. From Tables 3 and 4, the PV system efficiency \(\eta\) depends mostly on the ambient temperature for the two regions and the three field orientations. This result confirms the discussion provided above for the lower system efficiency in the near Riyadh region than that in the near Cairo region. Figure 4: System performance ratio of the PV system calculated over the 12 months for three orientations of the two regions. Figure 5: Energy produced by the PV system and available for usage over the 12 months for three orientations of the two regions. \begin{table}
\begin{tabular}{c c c c} \hline
**Response** & **Azimuth 0** & **Azimuth 20** & **Azimuth 30** \\ \hline \(\eta\) & \(T_{A}\) (81.5\%) & \(T_{A}\) (90.5\%) & \(T_{A}\) (73\%) \\ \hline \(PR\) & \(T_{A}\)\(Y_{a}\) (90\%) & \(G_{eff}\)\(Y_{a}\) (96\%) & \(G_{eff}\)\(Y_{a}\) (80\%) \\ \hline \(E_{prod}\) & \(G_{eff}\) (99\%) & \(G_{eff}\) (92\%) & \(G_{eff}\) (95\%) \\ \hline \end{tabular}
\end{table} 
Table 3: Most significant factors on the three responses for the three orientations near the Cairo region. In addition, from Tables 3 and 4, the energy produced by the system and available for usage \(E_{pred}\) is mostly affected by the global effective radiation \(G_{eff}\) and the array yield \(Y_{a}\), which is actually related to \(G_{eff}\). However, the most significant factors on the PV system performance ratio \(PR\) varies from one region to the other and from field one orientation to the other. For this variability, the performance ratio is chosen to be used for the reliability study to predict the lifetime of the PV system at both regions with the three different field orientations. Some of results obtained from the factorial design experiments to form the equations are shown in Table 3. A response is given by the summation of the obtained absolute value and the factors multiplied by the obtained coefficients. This table shows the coefficients of the factors and their combinations obtained for the field orientation (30\({}^{\lx@math@degree}\), 0\({}^{\lx@math@degree}\)) of both regions. From this table, the PV system efficiency in near the Riyadh region at field orientation (30\({}^{\lx@math@degree}\), 0\({}^{\lx@math@degree}\)) is given by:  
\[\eta=12.4241\;+\;-0.7815T_{A}\;+\;+0.0709V_{w}\;+\;+0.0434Y_{a}\;+\;+0.0409G_{ eff}.T_{A}+\ldots\]  
The most significant factors are highlighted in Table 5, which confirms the results obtained based on the \(p\) values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Response** & **Azimuth 0** & **Azimuth 20** & **Azimuth 30** \\ \hline \(\eta\) & \(T_{A}\) (97\%) & \(T_{A}\) (90.8\%) & \(T_{A}\) (90\%) \\ \hline \(PR\) & \(T_{A}\) (97\%) & \(T_{A}\) (95\%) & \(T_{A}\) Y\({}_{a}\) (94\%) \\ \hline \(E_{pred}\) & \(G_{eff}\) (99\%) & \(G_{eff}\) (99\%) & \(Y_{a}\) (100\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Most significant factors on the three responses for the three orientations near the Cairo region.