## 2 Theoretical Background
### Quantitative Methods
Despite its complexity due to the various models designed and being algorithmic, this approach considers both the evaluation of the overarching PMM and the concept of comparing performance indicators. [PERSON] and [PERSON] [24] presented a KPI-based approach for improving the company processes; performance requirements on company processes are specified as KPIs with target values that must be achieved within specific periods. To improve business processes, their evaluation is a necessary and fundamental step, as the latter provides various measurements that indicate whether or not business objectives have been achieved. Furthermore, BPM (Business Process Modeling) enables companies to understand their internal business processes better using a graphical notation and communicate them in a standardized way. BPM allows business processes to be designed, monitored, configured,and evaluated [25]. An essential aspect of the life cycle of such methods is performance evaluation [26] ([PERSON] and [PERSON], 2009). The proposed methodology is a BPM cycle in which the life cycle of KPIs is highlighted. The KPI measurements allow the process and recommendations of the proposal to be evaluated, which would help users improve their projects' performance and make the right decisions. In the work of [PERSON] et al. [27], a method for implementing KPIs to improve energy efficiency in the manufacturing sector was presented. This methodology aims to verify the accuracy of KPIs in the first instance and then proceed to the subsequent implementation. This procedure is necessary to avoid misinterpretations, forced redundancies, dark sides and failures. The work consists of a subsequent series of checks to validate the KPI calculation: the first check inspects the resulting unit of the KPI (a complete analysis helps to reveal inconsistencies); the second check is based on a comparison between the current and desired value. The validation process analyzes the indicator's ability to easily deduce potential improvement measures and the corresponding fields of action to improve the company's performance at various levels. Aligning the KPI with specific or overall targets is of interest to verify whether the achievement of the target is realistic. [PERSON] et al. [28] presented a method to measure and evaluate performance within the strategic management perspective. The study aims to assess performance metrics in detail and discover strategic decisions' effects on implementation. A performance measurement questionnaire was conducted in the company; the results were then evaluated to create a model for process improvement. It was defined how strategic decisions made due to five different situations would affect the efficiency of the company and the critical importance of strategic management. Such a framework consists of a method of considerable complexity that nevertheless assumes a periodic (thus significant) recalculation, considering both KPI comparison and industrial PMM evaluation. Such a method may be a candidate for analysis. On the other hand, the work of [PERSON] et al. [29] presented a hierarchical structure of KPIs for production management and continuous improvement of such systems. Their paper proposes a hierarchical structure for categorizing KPIs and identifying and analyzing their inherent relationships. Indicators and their measurement elements are classified at various levels, thus exploring the intrinsic pairwise relationships between KPIs. This structure provides a valuable tool for measuring, analyzing and utilizing KPIs. This methodology brings a straightforward system to implement, a periodic review and presents a method for comparing indicator values. However, it should be noted that it lacks the consideration of internal and external perspectives and the evaluation of the measurement system above.