## 6 The Mathematical Approach for Computing the Dependability of the Solar Tracking System
### Maintenance-Oriented Metric System for Reducing the Mean Time to Repair  
Maintainability metrics are less prevalent in hardware than in software development, but they are still useful to examine and improve the maintainability of hardware systems. Hardware maintainability metrics assess the efficiency with which hardware components, systems, or equipment may be maintained, repaired, upgraded, or expanded. This section extends the previously mentioned fault coverage-aware metrics with a novel maintenance-oriented metric system that uses several hardware assets such as modularity, accessibility, and predictive maintenance devices. The modularity factor (\(MF\)), derived from the aforementioned features, serves as a metric employed to measure the modularity of a solar tracking system. Modularity refers to the extent to which a system is composed of separate, interchangeable, and independently replaceable components. A higher modularity suggests a system design that allows for easy replacement or upgrading of individual components without affecting the entire system. Mathematically, the \(MF\) value can be expressed as in Equation (15):  
\[MF=\frac{N_{MC}}{T_{NC}}\times 100 \tag{15}\]  
In the context of Equation (15), \(N_{MC}\) refers to the count of components within the solar tracking system that are designed to be modular, meaning they can be easily detached, replaced, or upgraded, and \(T_{NC}\) is the overall count of components in the solar tracking system, regardless of their modularity. The accessibility score (\(AS\)) serves as a metric employed to measure the ease with which maintenance personnel can access components within a solar tracking system. This metric is geared towards assessing the accessibility of components, a factor that significantly influences the efficiency of maintenance and repair tasks. A higher \(AS\) signifies a system design that enables straightforward access to components, thereby reducing downtime during maintenance activities. The \(AS\) can be written as in Equation (16):  
\[AS=\frac{N_{AC}}{T_{NC}}\times 100 \tag{16}\]  
In the context of Equation (16), \(N_{AC}\) refers to the count of components within the solar tracking system that are easily reachable or removable during maintenance activities,and \(T_{NC}\) is the overall count of components in the solar tracking system, regardless of their accessibility. Predictive maintenance efficiency (_PME_) is a metric used to measure the effectiveness of predictive maintenance capabilities within a solar tracking system. Predictive maintenance involves the use of sensors, test devices, and data analytics to monitor the condition of components and predict when maintenance should be performed, allowing for proactive maintenance activities. A higher _PME_ indicates a system that efficiently utilizes sensors for predictive maintenance, contributing to reduced downtime and improved reliability. The _PME_ metric can be mathematically expressed as in the following formula:  
\[PME=\frac{N_{TD}}{T_{NC}}\times 100 \tag{17}\]  
In the context of Equation (17), \(N_{TD}\) refers to the count of sensors and test devices within the solar tracking system that are specifically utilized for predictive maintenance purposes. Finally, the \(T_{NC}\) is the overall count of sensors in the solar tracking system, including those used for various purposes, not just predictive maintenance. By combining the aforementioned metrics regarding modularity, accessibility, and predictive maintenance, we can define the _MI_ variable which describes the maintainability of solar tracking systems:  
\[MI_{Overall}=w_{1}\cdot MF+w_{2}\cdot AS+w_{3}\cdot PME, \tag{18}\]  
where \(w_{1}\), \(w_{2}\), and \(w_{3}\) are the weighting factors assigned to each metric based on their relative importance, and the values of \(MF\), \(AS\), and _PME_ range from 0 to 100.