## 3 Case Study Application
### WWTP Application and Modelling
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Equipment** & **Code Name** & **Description** \\ \hline Self-cleaning Screen & SS1 and SS2 & Large solids removal. \\ Cyclone Separator & CS1 & Medium inorganic solids. Removal such as grit, sand, and gravel, among others. \\ Primary Clarifier & PC1, PC2, PC3, and PC4 & Removal of settable organic solids. \\ Anaerobic Basin & NB1 and NB2 & Phosphorus removal. \\ Aerobic Basin & AB1, AB2, AB3, and AB4 & Aerobic biodegradation of organic contaminants. Oxygen allows bacteria to perform biodegradation processes. \\ Secondary Clarifier & SC1, SC2, SC3, and SC4 & Removal of settable organic solids. RAS is conveyed to the secondary biological treatment. \\ Disinfection Mixing Unit & DU1 & Desinfects effluent from the secondary clarifiers using chlorine before dechlorinating and releasing to the environment. \\ Primary Digester & PD1, PD2, and PD3 & Bacteria degrade organic waste into water and gases. \\ Secondary Digester & SD1, SD2, and SD3 & Undigested organic waste from the primary digester is degraded. \\ Gravity Belt & GB1 and GB2 & Partial water removal from digested waste. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Equipment Description. Figure 1: Operational Layout and Configuration of the WWTP. * Level 4: This includes all the equipment of the system, this is, the Self-cleaning Screens (SS1 and SS2), Cyclone Separator (CS1), Primary Clarifiers (PC1, PC2, PC3, and PC4), Anaerobic Basins (NB1 and NB2), Aerated Basins (AB1, AB2, AB3, and AB4), Secondary Clarifiers (SC1, SC2, SC3, and SC4), Disinfection Mixing Unit (DU1), Primary Digesters (PD1, PD2, and PD3), Secondary Digesters (SD1, SD2, and SD3), and Gravity Belts (GB1 and GB2). * Level 3: This level includes the subsystems clustered into the secondary biological treatment, this is, Biological Nutrient Removal (BR) and Aeration (AX). * Level 2: This level includes all subprocesses from the main process, this is, the Screening Process (SP), Grit Removal (GR), Primary Clarification (PC), Secondary Biological Treatment (ST), Secondary Clarification (SC), Disinfection (DX), Primary Anaerobic Digestion (PD), Secondary Anaerobic Digestion (SD), and Thickening Process (TP). * Level 1: This level considers the system as a whole. Figure 2 explains the hierarchical levels of the plant. Note that level 3 only exists because of the existence of two subprocesses, Biological Nutrient Removal (BR) and Aeration (AX), within the Secondary Biological Treatment (ST). In contrast, the rest of the processes only consist of the process itself. Figure 3 shows the expected availability of the system, subsystems, and individual elements. Figure 2: Hierarchical breakdown of the WWTP. Finally, using the availability indexes, the operational effectiveness impact (OEI) for each element is calculated, which is the loss percentage of either availability, production, or operational capability in the top-level. As it was described in the Section 2, the P-OEI and EOI of the system (top-level) will always be 100%. In other words, P-OEI is the quantified involvement of each element to the ineffectiveness of the system quantified as the potential capacity loss due to unavailability. On the other hand, the expected operational impact (EOI) is the expected responsibility or consequence if the said element should fail. The results are presented in Figure 4.  
Figure 3: Upstream Analysis: Availability. The results show that elements with higher P-OEI indexes (fourth level P-OEI) are the Cyclone Separator (22.75%), Disinfection Mixing Unit (20.91%), and Gravity Belts (9.24% and 10.54%, respectively), this means that these four elements are responsible for more than the 60% of the system's ineffectiveness, for example, the Cyclone Separator alone is responsible for the 22.75% of loss of production due to unavailability and EOI.