# A Predictive Reliability Model to Assess the Performance of Photovoltaic Systems
### Output and System Responses  
The output is the produced energy \(E_{prod}\) is available for usage and backup while the array is producing. This energy is given by:  
\[E_{prod}\ =\ E_{arr}\ -\ E_{lost}\ +\ E_{full}\]  
where \(E_{arr}\) is the energy at the output of the array while the battery is charging, \(E_{lost}\) is the energy losses due to conversion and wiring, and \(E_{full}\) is the unused energy due to full-battery loss. The system responses are the specs used to assess the system and include:  
1. System efficiency \(\eta\): the ratio of the produced energy to the irradiance on the total area of the collector and given by: \[\eta\ =\ \frac{E_{prod}}{G_{i}}\]2. System performance ratio (_PR_): the ratio of the produced energy to the energy that would be produced if the system is continuously working at its nominal STC efficiency. The performance ratio is also given by the ratio of the system yield to the reference yield. This ratio indicates the quality of the system regardless of the incident irradiance. The PV system was analyzed and assessed using different methods. Among these methods are the artificial neural networks (ANN), the adaptive neuro-fuzzy inference system (ANFIS), and others mentioned below for review. In this work, the PV system performance was analyzed by the reliability of this performance. Although reliability engineering is a famous and robust technique, it is not found in the literature. The aim of this study is to predict some measurements based on the system functionality to be used for optimum settings and system assessment. [PERSON] et al. [6] suggested an approach to maximize the total number of solar panels in a PV system in a given area without compromising the overall system efficiency, while also enhancing the output energy. The authors of this work achieved this by optimizing the installation parameters such as pitch, tilt angle, altitude angle, shading and gain factor, aiming to improve energy yield. In [10], the authors studied the effects of using a system for sun tracking of multi-axis type on electrical generation to evaluate its performance. The authors of this work investigated the effects of tilt angles and azimuth on the output power of a PV module. They estimated the instantaneous increments of the generated power when the PV module is mounted on a single- and dual-axis tracking system. The results they obtained showed that the yearly optimal tilt angle of a fixed panel facing the south is approximately 0.9 times the latitude of the city they considered. The slope of the panels of a photovoltaic system was studied in [11] for three cities. They utilized the Liu and Jordan model to obtain the monthly optimal angle of tilt. The results they obtained showed that the optimal tilt angle for these cities is less than 5\({}^{\circ}\). Optimizing the performance of a model based on an artificial neural network to estimate the solar radiation in the eastern region of Turkey is provided in [12]. They discussed the estimation of performance by different types of neural networks. The work of these authors aimed to evaluate the use of a neural network for such an optimization problem. A code-based modeling approach was proposed in [13] to help study PV technologies. The authors used a synthesized dataset for the coding and training of the model. They used commercial PV modules to validate the model they suggested. Using this model, they repeatedly and reliably predicted the maximum power point, short circuit current and open circuit voltage with <2%, 0%, and <10% deviations, respectively. In [14], [PERSON] et al. proposed an ANFIS (adaptive neuro-fuzzy inference system) to identify the most significant parameters to predict the daily global solar radiation. The ANFIS is a process to select variable input parameters with 1, 2 and 3 inputs to identify the most significant sets for three cases.