# PAL-VMEA: A Novel Method for Enhancing Decision-Making Consistency in Maintenance Management
## 5 The Proposed PAL-VMEA Method Conjugated with BWM
After defining the weights of the skills (constructive basis of extractors of belief and disbelief), PAL2v is applied through a structured table containing the Sub-KPCs and NFs to be evaluated (according to the failure modes) of each KPC. Thus, the decision-makers assign a value from 0 to 1 (0 meaning total disbelief and 1 total belief) for each value of the VMEA criteria (Tables 3-5). This process is repeated for the evaluation of each KPC with the purpose of assigning the initial belief weight value (\(a_{ij}\)) and subsequently, the determination of belief and disbelief (\(b_{ij}\)) using the extractors developed in the presented method. 4. The weights added to the decision-makers' skills are used in the extraction of belief (favorable evidence) and disbelief (unfavorable evidence) during the application of PAL2v. The belief and \begin{table}
\begin{tabular}{l c} \hline \hline
**Criteria** & **Weight** \\ \hline Very low sensitivity. A change of in noise factor is very unlikely to cause a significant deviation in Sub-KPC & 1–2 \\ Low sensitivity. A change in noise factor is unlikely to cause a significant deviation in Sub-KPC & 3–4 \\ Moderate sensitivity. A change in noise factor is quite likely to cause a significant deviation in Sub-KPC & 5–6 \\ High sensitivity. A change in noise factor is likely to cause a significant deviation in Sub-KPC & 7–8 \\ Very high sensitivity. A change in noise factor is very likely to cause a significant deviation in Sub-KPC & 9–10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Criteria for assessing the sensitivity of Sub-KPC to noise factors [32]. disbelief extractors have the purpose of extracting uncertainties during the decision-making process from the values to be attributed to the failure modes. With the belief input value (\(a_{ij}\)), the disbelief (\(b_{ij}\)) is calculated, then the belief extractor (\(be_{ij}\)) and disbelief extractor (\(de_{ij}\)) are applied to these values (considering a scale from 0 to 10), using Equations (5)-(7), considering \(W_{1}\) and \(W_{2}\). In the final result, a weighted average of the extractors is computed. \[b_{ij} =1-a_{ij} \tag{5}\] \[be_{ij} =a_{ij}\cdot W_{1}\] (6) \[de_{ij} =b_{ij}\cdot W_{2}. \tag{7}\]  
To calculate the result for favorable (or belief, \(a_{w}\)) and unfavorable (or disbelief, \(b_{w}\)) evidences, both values obtained by the extraction process for each Sub-KPC and NF, a weighted average of the extractors is computed. In addition, for the estimation of the degree of certainty (\(H\)) and uncertainty (\(G\)), a degree of requirement (for decision-making considering the most consistent weight) must be established (generally, 0.5, i.e., a minimum of 50% of opinions must converge with certainty so that the value is established in the Truth zone). The requirement level determines the consistency of the analysis or the degree of caution to use the analysis, which depends on the further use of the results (such as an indicator for decision-making) and its implications. For a level of requirement of 50%, assessments will be carried on with at least 50% of certainty. Thus, the weight of each Sub-KPC and NF is established by the highest degree of certainty (\(H_{max}\)), with the indicators obtained by Equations (8) and (9). \[H=a_{w}-b_{w} \tag{8}\]  
\[G=(a_{w}+1)-b_{w}. \tag{9}\]  
If the same degree of certainty (\(H\)) is obtained for different weights, i.e., there is a contradiction of opinions establishing total indeterminacy (same level of favorable and unfavorable evidence), decision-makers should search for more information about the particularities of the analyzed variable for decision-making (and new weight assignment).