## 6 The Mathematical Approach for Computing the Dependability of the Solar Tracking System
### Fault Coverage-Aware Metrics for Reliability Evaluation  
As solar tracking systems comprise electrical components prone to hardware faults like stuck-at or delay faults, particular emphasis is placed on evaluating the reliability of pivotal components such as the MCU, responsible for controlling axis rotations through a dedicated motor driver. This research delves into the possibility of precisely computing the SRF parameter using the proposed RBILBO solution, drawing upon three novel fault coverage-aware metrics introduced in earlier studies [66; 67; 69].  
Evaluating availability and reliability in PV systems entails scrutinizing failure data amassed during field testing. These data are then utilized to forecast maintenance costs for forthcoming equipment repairs. Similarly, experimental data derived from the RBILBO solution are leveraged to delineate hardware fault coverage. Fault coverage denotes the percentage of tested vectors compared to the total number of test patterns. The formula for calculating fault coverage (\(FC\)) is outlined in Equation (9) [79]:  
\[FC=\frac{T_{V}}{T_{P}}\times 100\%, \tag{9}\]  
where \(T_{V}\) represents the number of test vectors, whereas \(T_{P}\) signifies the count of tested patterns. Furthermore, a hardware detection ratio is introduced, designated as \(DR\), and is expressed as depicted in Equation (10) [79]:  
\[DR=FC\times N_{P}, \tag{10}\]  
where \(FC\) represents the hardware fault coverage, and \(N_{P}\) stands for the total number of test patterns. The detection ratio holds significance as it facilitates the computation of the solar test factor (\(STF\)) within the fault coverage-aware metrics equation set. The \(STF\) parameter for hardware test scenarios can be mathematically expressed as shown in Equation (11) [79]:  
\[STF_{H}=\frac{DR}{2^{D}} \tag{11}\]  
In Equation (11), \(D\) represents the number of \(D\) FFs utilized in the MISR's hardware design. However, Equation (11) serves as a universal formula and necessitates suitable adjustments to account for single SaFs, double SaFs, and triple SaFs accordingly. Thus, the original metrics system [64] undergoes modification to align with the requirements of the three-test scenario, as outlined in Equation (12) [79]:  
\[\left\{\begin{array}{l}STF_{SaF_{1}}=\frac{DR_{SaF_{1}}}{2^{D}}\\ STF_{SaF_{2}}=\frac{DR_{SaF_{2}}}{2^{D}}\\ STF_{SaF_{3}}=\frac{ST_{SaF_{3}}}{2^{D}}\\ STF_{G}=\frac{ST_{SaF_{1}}+ST_{SaF_{2}}+ST_{SaF_{3}}}{3}\\ STF_{G}=\frac{DR_{SaF_{1}}+DR_{SaF_{2}}}{2^{D}}\\ STF_{G}=\frac{DR_{SaF_{1}}+DR_{SaF_{3}}+DR_{SaF_{3}}}{3^{2D}}\end{array}\right. \tag{12}\]Additionally, during the conducted experimental cases, the \(FC\) parameter increases according to the use of reconfigurability, thus eliminating the number of undetected errors, and can be written as in Equation (13) [79]:  
\[FC=100\%-ALS, \tag{13}\]  
where \(ALS\) denotes the aliasing factor employed to mask bit configurations that correspond to the golden signatures. Subsequently, the detection ratio is computed for each of the three test batches, according to Equation (14) [79]:  
\[\left\{\begin{array}{l}DR_{SaF_{1}}=FC_{SaF_{1}}\cdot N_{P}\\ DR_{SaF_{2}}=FC_{SaF_{2}}\cdot N_{P}\\ DR_{SaF_{3}}=FC_{SaF_{3}}\cdot N_{P}\end{array}\right., \tag{14}\]  
where \(SaF_{1}\), \(SaF_{2}\), and \(SaF_{3}\) are parameters that denote single, double, and, respectively, triple SaF models. SaF models are particularly useful in the design and testing of digital circuits because they provide a systematic way to evaluate the circuit's behavior under various fault conditions, helping to identify potential weaknesses or defects in the design. These models are also used in fault diagnosis to determine the location and nature of faults in a circuit based on its observed behavior.