## 3 Results & Discussion
### Case IV  
This case regards a true production system and it is used to test the validity of the algorithm in terms of the physical relationship between the PIs. This is done through forcing the Measured Values to create an KPI-level alarm and check whether the algorithm will find the root cause and indicate towards the correct Measured Value. Thus, a production system of thirty (30) identical machines that are arranged in eight work-centers has been simulated by a commercial software [42] (Figure 12). The system simulates a real-life machine-shop producing two variants of Cylinder Head parts: (a) Petrol and (b) Diesel. Different processing times and setup times have been configured. Additionally, negative exponential distribution for Mean-Time-Between-Failures (MTBF), and a real distribution on Mean-Time-To-Repair (MTTR) considered the equipment breakdown on machines. Customer demand has been set by a normal distribution. Finally, the performances have been recorded and manually fed in the informational model. Figure 11: Case III. Top: Evolution of KPI, Middle: Evolution of PIs, Bottom, Contribution of each PI. Figure 12: Workcenters arrangement of the production system. The number indicates the amount of machines for each workcenter. The KPIs that are utilized in this case study (top to bottom) are mentioned below and their relationship is also given in Figure 5, beginning with Overall Equipment Efficiency (OEE). * OEE = Availability \(\times\) Effectiveness \(\times\) Quality Rate
* Availability = Actual Production Time/Planned Busy Time
* Effectiveness = Processing Time/Actual Production Time
* Quality Ratio = Good Quantity/Produced Quantity
* Actual Production Time = Processing Time + Setup Time + Handling Time  
A simulation has been conducted with the machine breakdowns deliberately increased with time. Subsequently, the algorithm of finding the root-cause is run once. In Figure 13, it is clearly shown (yellow shaded rectangles and curved arrows) that the algorithm dictates the major role of Effectiveness. This definitely helps in pointing out the direction that the production manager should focus on. As a matter of fact, if one repeats the procedure of running the algorithm, but this time utilizing Effectiveness instead of OEE (68% contribution), and then the Measured Value that comes up is Processing Time. This means that the engineer should focus on why the machines do not work that much, which is indeed the root cause of the OEE drop (Figure 13). It seems that the algorithm works successfully without setting any rules or training. On the contrary, in the literature, works coming up often have to use one or the other, so a direct comparison cannot be made. For instance, in another alarm root cause detection system [43], the authors, even though they are describing the impact on case studies in brief, explicitly point out the need for rules in an internal expert system. Additionally, the use of KPIs at process level [44] is complementary to the current work. A framework that aims to detect the quality of the process, as per classifiers utilizing depth of cut and spindle rate could be integrated; corresponding indicators can be regarded as processed Measured Values. Additionally, the issue of validity of the indicators that are aggregated from IoT is also an issue that has not been raised herein, as the data have been considered to be valid. In addition to this, architectures that are based on complexity handling [45] and algorithms, such as Blockchain [46], can guarantee this goal, while, as indicated by corresponding results in literature [47], the introduction of a manipulation strategy, such as KPI-ML, will boost the performance of any algorithm, including the current. In other pieces of literature [48], the Multiple Alarms Matrix is utilized and hierarchical clustering is applied. In their results, they seem to be presenting the usability of the method towards the correlation of the alarms and extraction of the unique ones.