## 3 Proposed Methodology
### Thermoeconomic Diagnosis
#### 3.2.3 Impact of Each Anomaly  
Once the equipment with intrinsic anomalies has been identified, the next step is to quantify the impact of these anomalies on the rest of the system components. This process is classified into two fundamental cases: (1) when there is only one anomaly; and (2) when multiple anomalies exist.  
Assessment of a Single Intrinsic Anomaly  
When only one intrinsic anomaly is detected in the system, its influence on the other components can be analysed directly. As mentioned above, an anomaly induces changes in the intermediate thermodynamic variables (\(\overline{x}^{OP}_{i}\)) of the other components, which causes the rest of the components to adjust their operation to the new anomalous condition, causing induced cost overruns \(\Delta k_{ind,i}\) with respect to the reference situation. To evaluate how an anomaly affects the other components, it is sufficient to compare the unit consumptions of each component i, obtained by means of the reference operators (\(k_{i}^{B,ref}\left(\overline{x}_{i}^{OP}\right)\)) and the unit consumptions in the global reference system (\(k_{i}^{R,ref}\left(\overline{x}_{isi,i}^{REF}\right)\)). Thus, the consumptions of each intermediate component obtained from the intermediate variables in operation \(\overline{x}_{j}^{OP}\) and in reference of the global system \(\overline{x}_{isi,i}^{REF}\) are compared by distinguishing the effects of the intrinsic anomalies (\(\Delta k_{i,anomaly}\)) and the effects of induced anomalies (\(\Delta k_{i,ind}\)).  
Assessment in the Presence of Multiple Intrinsic Anomalies  
In the scenario where several intrinsic anomalies are identified, the strategy consists of an iterative process of \"repairing\" the anomalies, addressing them one by one until a state with a single anomaly is reached, where the procedure of the previous section is reproduced (a single intrinsic anomaly).  
The idea is that, by \"repairing\" an intrinsic anomaly, the induced effects of that anomaly on the overall system will also be eliminated. This approach implies, after identifying a component with an anomaly and quantifying its intrinsic cost overrun through its operator (\(\Delta k_{anomaly,i}=k_{i}^{A,op}-k_{i}^{B,ref}\)), progressively implementing its reference curves (\(k_{i}^{REF}=f\left(\overline{x}_{j}^{REF}\right)\)) in the overall system operation, so that the anomaly is avoided and the reference and new operation curves (\(OP_{sist}^{\prime}\)) are the same (\(k_{i}^{REF}=k_{i}^{OP}\)).  
For example, if anomalies are initially detected in three components (boiler, exchanger and tank), the operating state of the system is virtually redefined (\(OP_{sist}^{\prime}\)) by considering only two components with anomalies (boiler and exchanger). Subsequently, the consumption of the system in the situation with three anomalies is compared to the situation with only two anomalies (\(OP_{sist}\)_vs_\(OP_{sist}^{\prime}\)), which makes it possible to identify the influence of the \"repaired\" tank component on the behaviour of the other components and on the overall consumption in terms of induced cost overruns (\(\Delta k_{ind,i}\)). This process is repeated, reincorporating the reference curve without anomalies of the heat exchanger (\(OP_{sist}^{\prime\prime}\)) to compare the system with two anomalies against one with a single anomaly in the boiler.  
This process, although intuitive, needs to determine a criterion for choosing the order in which the intrinsic component anomalies are \"repaired\". A logical criterion is based on calculating the absolute cost overruns generated by each intrinsic anomaly (\(\Delta C_{i}=c_{i}\cdot\Delta k_{i,anomaly}\cdot P_{i}^{ref}\)), with \(c_{i}\) being the unit economic cost of the \(i\) component and \(P_{i}^{ref}\) the product of component \(i\) in reference condition (which can be calculated at the beginning of the process with the \(OP_{sist}\) variables) and prioritising according to the component with the highest cost overrun to the lowest.