# Fleet Resilience: Evaluating Maintenance Strategies in Critical Equipment
## 3 Proposed Methodology  
To estimate the reliability, maintainability and total availability parameters of a complex engineering system, there are several ways to represent them. [PERSON] [42] proposes and compares fault tree analysis (FTA) and reliability block diagrams (RBDD). The FTA is a deductive methodology that allows the determination of possible causes of disruptive events in a system. In addition, this allows for the estimation of the probabilities of a failure. The FTA seeks to determine the causes of an undesirable event. Using \begin{table}
\begin{tabular}{c c} \hline \hline
**Configuration** & **Equation** \\ \hline Series & \(A_{s}(t)=\prod\limits_{i-1}^{1-n}A_{i}\) \\ \hline Parallel & \(A_{s}(t)=1-\prod\limits_{i-1}^{1-n}(1-A_{i})\) \\ \hline Partial Redundancy & \(A_{s}(t)=\sum\limits_{r=k}^{n}\left(\begin{array}{c}n\\ r\end{array}\right)A_{i})^{n-1}(1-A_{i})^{r}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Availability metrics according to different system topologies. Figure 5: System availability subject to degradation and shock (adapted from [12]). a fault tree as a basis, the system is dissected in detail to determine the root causes or combinations of causes of the superior event. Top events are generally significant failures, which generate serious consequences to system performance. The FTA produces both qualitative and quantitative information about the system under study. However, FTAs cannot be used to accurately estimate the value of system availability and are therefore only used to obtain good approximations of that parameter. [PERSON] et al. [43] defined the system availability considering a combination of \"AND gates\" and \"OR gates\". RBDs are representations based on linked blocks according to various configurations (series, parallel, stand by, etc.) or topologies, which, according to these links, and the reliability of the equipment or systems that are represented by each of the blocks, specifically affect the reliability of the system as a whole. Still, according to [PERSON] [42], in simple systems, the FTA and RBD methods usually produce similar results. In fact, [42] suggests equivalence relations between both methods. However, it should be mentioned that FTA is too difficult to apply for complex systems (back-up configurations, redundancy, etc.). Therefore, it can be deduced that the RBD method is more suitable as the systems' configurations to be represented become more complex. For the present work, the following steps were carried out:  
* Selection of the resilience metric. Implementation of the model using MATLAB software. * Modeling of the production system through reliability blocks diagrams (RBD) using R-MES software. * Obtaining the availability of the system using real data and reliability, availability and maintainability (RAM) analysis. * Simulation of different maintenance strategies and the insertion of additional equipment (Monte Carlo experiments). * Calculating and comparing resiliencies for each simulated scenario. The application of reliability block diagrams is proposed to support the availability calculations. With this methodology, in combination with Monte Carlo simulation experiments, it is possible to estimate the expected values of availabilities both at the equipment level and at the system level, taking into account the topological relationships among the equipment pieces [44]. In addition, through these experiments, it is also possibly useful information of which components contribute to the major portion of capacity and availability losses. Finally, using such an approach, it is possible to execute the trade-offs and assessments among reliability, maintainability and redundancy. Here, we included in such evaluations the possibility of observation of the behavior of the system's resilience metric of the according to the previously mentioned system design parameters. [PERSON] et al. [12] required the definition or computation of the steady state availability for the application of their proposed model.