*3.5. Robustness and Statistical Analysis*

This section presents statistical evaluation based on mean, minimum, maximum, and standard deviation of RMSE for all previously implemented methods, and a comparison with respect to precision and consistency of the distinct algorithms in a total of thirty runs and depicted in Table 5. The mean of RMSE is calculated to evaluate the precision of algorithms, and the standard deviation is calculated to evaluate the consistency of the parameter estimation methods.


**Table 5.** Statistical results of RMSE of different algorithms for all three models.

The statistical results presented in Table 5 indicate that WOAPSO is the most accurate and reliable parameter optimization technique. As shown in Table 6, based on the Friedman ranking test result, the best ranking is obtained by the WOAPSO, followed by WOA, GWO, GSA, PSOGSA, SCA, and PSO. Also, Figure 8 shows the distribution of results (i.e., RMSE) obtained from the distinct algorithms in 30 runs in the form of a boxplot graph for the SDM, DDM, and PV module. It can be anticipated from Figure 8 that the proposed WOAPSO algorithm delivers the best results in terms of accuracy and reliability compared to the other six algorithms.

**Table 6.** Ranking of the proposed WOAPSO and other compared algorithms on three PV models according to the Friedman test.


**Figure 8.** *Cont*.

(**c**)

**Figure 8.** Boxplot graph of best RMSE in 30 runs for (**a**) single diose model (**b**) double-diode model (**c**) polycrystalline SS2018P PV module.
