## 2 Theoretical Background
### Comparative Analysis of Methods  
This section analyzes the methodologies set out above, drawing attention to which are applicable, and which are less so, depending on the various criteria chosen for their evaluation. Indeed, we aim to define the most suitable methodology for assessing coherence and designing a tree of indicators aligned with the company's strategic goals, which will then be validated through a case study. For this purpose, eight criteria were identified for evaluating the methods analyzed in the literature, deemed suitable for the task described above. The requirements were designed to identify the approach best suited to this work's scientific and industrial needs. The criteria chosen are:  
* Qualitative methodology: include contributions that do not use formulas, mathematical models and/or statistics;
* Quantitative methodology: include contributions that use formulas, mathematical models and/or statistics;
* Ease of implementation: represent a criterion that aims to identify how easy the method is to apply and implement in an organizational reality, therefore, an evaluation scale has been established to indicate this ease. The scale is numerically composed of integers ranging from 1 (complex implementation) to 3 (simple implementation);* Frequency of recalculation: represent a criterion set to understand the frequency with which the proposed approach requires the tree to be assessed, as it may vary and be modified by the company due to certain conditions. The rating scale chosen consists of the items: Static (indicates that the method does not envisage a subsequent recalculation), Dynamic (indicates that the approach envisages a recalculation not at constant intervals, but as certain underlying conditions change), Periodic (suggests that the method makes recalculations following the passing of regular time breaks);
* Inclusion of internal and external perspectives: represent a criterion that aimed at determining whether the methodology includes or not these perspectives;
* Validation of industrial PMM consistency: represent a criterion for assessing the consistency of the PMM indicates whether the listed procedures provide for such an assessment or whether it is absent, indicating this with a confirmation sign if yes. This criterion is necessary to identify whether the proposed method provides for an evaluation of the consistency of performance measurement systems;
* Comparison of KPIs: represent a criterion that aimed to check whether the approach provides for a comparison of KPIs and, consequently, the underlying indicators;
* Integrability of KAIs: represents a criterion that seeks to assess whether the method integrates KAI into its structure;
* Proposed methodology: represent the criterion concerning the proposed calculation methodology, indicating the quantitative or qualitative method used. The following division of the methods mainly found in the literature is adopted: decision support, algorithmic procedure, indicator validation procedure, Delphi panel or questionnaire, industrial PMM and strategic alignment. It is helpful to emphasize that the criterion concerning the possibility of integrating the method by taking Key Activity Indicators into account was also introduced into the analysis. However, none of the proposed methods takes them into account; some of them, due to their structure, present the possibility of being integrated into this sense. The importance of extending a method in this direction would make it possible to link KPI-KRIs with a set of KPIs by evaluating the strategic alignment of the PMM even more precisely. The analysis of the different criteria defined is now shown in Table 1, highlighting why this was chosen and its purpose.