This work is a statistical study of the broadband light absorption in thin film solar cells, enhanced by metallic surface nanotexturing. We consider optimum grating structures on the surface of amorphous silicon solar cells obtained by inverse optimization, and study the joint statistics of the resulting absorption enhancement/spectra in the presence of time and structural variants, such as fabrication error and year around changes in the solar irradiance, as well as the angle of incident. We adopt yearly data for solar irradiation at individual hours. In conjunction with the data for light absorption spectra at various incident angles and random samples of the fabrication error vector, we evaluate the real world performance of optimized solar cells. The resulting conclusions serve as a sensitivity/time analysis for better understanding the limits of performance and robustness of thin film cells and optimal light trapping mechanisms.