# On the Impact of Additive Manufacturing Processes Complexity on Modelling
## 3 Implementation and Primary Results
In Table 3, an indicative quality-based KPI has been selected for the aforementioned processes, along with the most common minimum and maximum values and the important step. For SLM and FDM, the KPI of temperature has been selected because the process mechanism of these particular process groups utilizes heating for the joining of the consecutive layers. In SLA, exposure has been selected, as it characterizes the success of the polymerization-based process mechanism. In concrete AM, a heuristic measure for quality based on the consistency and uniformity of the path dimensions has been selected; this KPI is described in [21]. The important step for each KPI has been selected to enable a representative resolution for the corresponding phenomena of each process. Following a similar procedure to that of the process parameters, an indicative number of different alternatives has then been calculated for the KPIs as well. More specifically, 81 alternatives were calculated for SLM owing to the minimum of 700 \({}^{\circ}\)C, maximum of 1500 \({}^{\circ}\)C and important step of 10 \({}^{\circ}\)C, as the difference of the temperature limits of the mushy region (between solid and liquid) [29] results in this value. The difference between the two temperatures, divided by the important step results in 81 alternatives. The indicative alternatives of FDM were calculated to be 8 for a temperature range of 60-175 \({}^{\circ}\)C and an important step of 15 \({}^{\circ}\)C. In SLA, which is not a thermal-based AM process, the nature of the process mechanism requires a constant exposure in order for the bonding to be successful. Therefore, the curing-depth KPI has been selected along with typical minimum and maximum depths. Finally, in concrete AM, the part consistency-quality metric (PCQM) has been selected as \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Process** & **Material** & **Performance Indicators** & **Min** & **Max** & **Important** & **Alternatives** \\  & & & & & **Step** & **(Max – Min + 1)/Step** \\ \hline SLM [26] & Steel & Temperature (\({}^{\circ}\)C) & 700 & 1500 & 10 & 81 \\ FDM [67] & PLA & Temperature (\({}^{\circ}\)C) & 60 & 175 & 15 & 8 \\ SLA [66] & Resin & Cure Depth (mm) & 0.35 & 0.55 & 0.05 & 24 \\ Cement-based AM [18] & Concrete & Part consistency–quality metric & 1 & 5 & 1 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Indicative quality key performance indicator (KPI) per process group along with minimum, maximum, important step values and alternatives calculation. the most representative KPI. The PCQM is a qualitative empirical metric, reflecting the consistency and quality of the extruded part [21], in terms of extruded part width variation and roughness. It ranges from 1 (implying bad quality) to 5 (for high quality). In Table 4, the joint Shannon entropy of the alternatives has been calculated for each process. For this calculation, the alternatives of the process parameters (Table 2) and of the KPIs (Table 3) of each process have been used based on the following equation:  
\[H(X,Y)=\frac{\log(X\ Y)}{\log(2)} \tag{6}\]  
where \(H\) is the joint entropy of the process parameter (X) and KPI (Y) of each process. The results of this calculation yield the total entropy of each process joint with temperature, which is an indicative measure of motion complexity regarding its effect on part quality (Table 4). These results indicate the complexity of the process mechanism regarding the impact of the process-parameter selections on the most representative quality-related KPIs. It may be observed that the indicative process of the metal-based AM group (SLM) has the highest value of process PP-KPI coupled complexity. It is followed by the indicative processes of the cement-based AM and plastic-based AM. The resin-based AM has the lowest total-entropy value, as there is a very strong PP-KPI connection and the best results are given when a strict relationship is maintained. Another aspect of the process complexity that should be considered is the spatial complexity of the process mechanism.