## 1 Introduction  
According to [1], a fault can be defined as \"an abnormal condition that may cause a reduction in, or loss of, the capability of a functional unit to perform a required function\". Faults in photovoltaic (PV) installations can significantly affect their energy yield, which is why the development of fault detection and diagnosis techniques has become an essential topic of research in recent years, Refs. [2, 3, 4]. Research works that analyze failure mode in solar modules, e.g., Refs. [5, 6, 7, 8, 9, 10, 11], have identified that the power reduction in PV modules under fault causes a deformation of the current-voltage curve, e.g., curves in [12]. Recently, Ref. [13] presented a performance analysis with 30 faulty modules of different brands. The study shows that, on average, the power loss after two years, with several faults, drops around 1.08%; also, the voltage variation at maximum power was, on average \(-1.17\%\). Similar research in India concluded that, on average, power degradation in PV modules is found to increase 1.4% per year over 25 years [14]. But this degradation rate is not a static value; it depends on the life stage of the PV installations as is shown in [15], the first 18 years around 0.1% per year; then the next period of 10 years, the rate raises around 1%/year, and the final life stage, the rate increases more than 1.2%/year. It is important to highlight that failure modes at the module level affect the whole PV installation performance because the PV array is a symmetrical composition of PV modules as is demonstrated by [PERSON] in [16]. Eighteenth types of faults in solar modules have been described in [17], their detectable effects sometimes overlap, so it is not easy to distinguish among them. Furthermore, the diagnoses of faults require combining knowledge of different domains (visual inspection, thermography, electrical, chemical, material analyses, so on), Refs. [18, 19]. This means that the specific failure modes could have, for example, the same behavior in the electric domain. The detection criterion used in this paper is based on the widely accepted five parameters model, which, according to [20], can represent a single solar cell or several cells connected in series (PV module). This model is mathematically represented as follows,  
\[I=I_{ph}-I_{s}\left(e^{\dfrac{V+IR_{s}}{N_{s}\eta V_{t}}}-1\right)-\dfrac{(V+IR_{ s})}{R_{p}} \tag{1}\]  
where \(I\) and \(V\) represent the current and voltage of the module, \(I_{ph}\) is the photo-current generated, \(I_{s}\) is the saturation current of the diode, \(R_{s}\) and \(R_{p}\) are the parasitic series and parallel resistances, \(N_{s}\) is the number of cells in series, \(\eta\) represent the ideality factor, and \(V_{t}\) is the thermal voltage. An increase in the PV module series resistance can model several fault mechanisms, as it has been indicated in [21; 22]. However, using other parameters to explain other failure modes is scarce in the literature. In this regard, one of the contributions of this work is to propose parameter ranges in the PV model that represent others failure modes not included in the typical models, e.g., only series resistance variation. This work will focus on the most common types of degrading faults listed next. * Series resistance degradation (SRD) faults. The increase of the parasitic resistance \(R_{s}\) could be expected by thermal cycling, solder corrosion, broken ribbons, and homogeneous soldering disconnection, so on. For example, Ref. [23] indicates that normally the increment is 10 %/year. However, the variation of \(R_{s}\) could be up to ten times its original value, according to [24]. * Optical homogeneous degradation (OD) faults. The photocurrent \(I_{ph}\) is affected by homogeneous glass corrosion, homogeneous contamination, loss of transparency, homogeneous corrosion of the anti-reflection coating. For instance, the yellowing and the browning are faults that cause power losses up to 50% [25].