## 2 Methodology  
The methodology [13; 14] proposal performs an analysis based on an RBD [19; 20] configuration and desegregates the overall process into levels in which the highest level represents the system itself, and the lower levels represent singular indivisible units. More specifically, the availability analysis is performed from the lower levels to the highest, running from the singular elements to the system itself. On the contrary, impact analysis is carried out from the highest level (system) to the lower levels (indivisible units). Moreover, during implementation and analysis, the methodology should also account for the joint processes necessary for the identification of improvement opportunities regarding maintenance activities and suggest recommendations for maintenance and sustainability. Summarizing, these activities and considerations can be abridged into four milestones of the analysis:  
1. Data Management: correct or remove inaccurate and missing data. Collect, store, and organize useful data. 2. RAM Analysis: upstream analysis of availability and reliability. 3. P-OEI Analysis: downstream analysis of operational effectiveness accountable for propagation effects. 4. Decision Making: result and analysis evaluation to make decisions regarding maintenance and operations. Adapting the proposed methodology to the specific case of a WWTP, an upstream analysis is performed to calculate RAM indicators starting from the lowest level units building up to the entire system using logical dependencies of the RBD [19; 20]. A second stage analysis is carried out from the highest level (system) and goes downstream to the lowest level units quantifying the impact on operational effectiveness through production capacity loss or level of contaminant removal in the case of a wastewater treatment plant [21]. In this manner, by assessing all possible scenarios and the likelihood of each scenario for complex configurations, it is possible to calculate the P-OEI and the contribution produced by each element to the lack of effectiveness of the system based on production loss due to unavailability and the expected operational impact (EOI). The latter explains how failure or unscheduled stoppages may impact the effectiveness of the system. Stage 1: Upstream RAM analysis starting from indivisible elements or singular machines (lowest level) escalating to the overall system by using RBD methodology to carefully account for the functional dependencies and adequate mathematical relations to compute reliability and availability. The latter of which is an expression of the probability that in a given window of time, the equipment will be available as required [22]. Considering the latter and under the assumption that required equipment must always be operational and that the work orders are immediately executed after failure, the expected availability of any equipment is [13; 14]:  
\[A_{i}=\frac{MTTF}{MTTF+MTTR} \tag{1}\]  
where  
\(A_{i}\): expected availability of the equipment. \(MTTF\): mean time to failure of the equipment. \(MTTR\): mean time to repair of the equipment. When calculating availability for any series configuration subsystem, the functional dependency of the elements of must be accounted for. Therefore the availability of the subsystem is as follows:  
\[A_{series}=\prod_{i=1}^{n}A_{i} \tag{2}\]  
Regarding subsystems in full redundancy configuration (parallel), which is characterized by the simultaneous operation of each element and the capability of each element to withstand 100% of the workload, the following expression is considered for a redundant non-reparable system:  
\[MTTF_{parallel}=\frac{1}{\lambda_{1}}+\frac{1}{\lambda_{2}}-\frac{1}{ \lambda_{1}+\lambda_{2}} \tag{3}\]  
where  
\(\lambda_{i}\): average failure rate of each piece of equipment that participates in the system.