**4. Conclusions**

This paper presents an approach for identifying the measured values that may negatively a ffect the production performance by eliciting historical data with the aid of Key Performance Indicators. Di fferentials have been adopted to this e ffect, being implemented in the developed dashboard and applied to a data set generated by simulation. To achieve this, performances have been stored into an RDBMS system and they have been aggregated through an OLAP server. The key advantage of the method is the quick identification of the root measured value, which will lead the production performance to undesirable directions from the ones expected by the managers, but in a non-supervised way. Therefore, it provides a technique for the development of functional dashboards beyond the visualization of accumulated indicators. Additionally, this paper proposes that dashboard applications, despite being complex and perhaps becoming cluttered up, could be used for automated decision support, as in the case of production performances. The results have shown that managers using the dashboard may be alerted about the weaknesses of their production performance before it is actually done at the shop-floor.

It seems that a digital twin for real time managemen<sup>t</sup> of production alarms is feasible, and the algebraic notion of di fferentials is a powerful tool towards this direction. It covers several aspects of a digital twin; it uses the data themselves instead of elaborated models, it is deterministic towards variations (by default), it is immune to noise (at least in the described examples), and, of course, it can be used in loops of automated decision making. However, the use of Human-In-the-Loop Optimization techniques might be inevitable, as the actions derivation, as well as triggering of the tool, may have to include the knowledge that operators have accumulated.

Regarding extensions of the work, knowledge-based libraries for action identification have to be implemented as a continuation to the current approach. Additionally, it seems logical that, besides the mean value, moments of higher order, such as variance, skewness, and kurtosis, could be elaborated to assist decision making. However, the interpretation of these values exceeds the purposes of this study. Another extension is that of the di fferential order. Derivatives of any order, as well as integrators, could be used to enrich the information that is given to the user. In addition, it has to be mentioned that the definition of the relations between the KPIs is of grea<sup>t</sup> importance both to the calculation and to the interpretation of the di fferentials.

**Author Contributions:** Conceptualization, P.S. and D.M.; Formal analysis, P.S.; Methodology, A.P.; Software, A.P. and C.G.; Supervision, D.M.; Writing—original draft, A.P. and C.G.; Writing–review & editing, D.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding. **Conflicts of Interest:** The authors declare no conflict of interest.
