# Semantic Modeling Approach Supporting Process Modeling and Analysis in Aircraft Development
## 5 Discussion
### Qualitative Analysis  
From a qualitative perspective, compared with the traditional avionics system development process planning using documents, the given approach can describe the development process of the avionics system and provide decision-making options for project managers by implementing the static and dynamic analyses. The KARMA language is a textual and semantic modeling language with meta-metamodeling capability developed based on the GOPPRRE meta-metamodels. It supports the construction of metamodels for development process from different domains and process modeling specifications with strong model description capability and expansibility. In this study, we built a BPD model that supports the process description of the aircraft avionics system, satisfying the product life cycle design process of the 15,288 specifications, such as tasks of system design and system requirements definition. However, it describes symbols in the BPMN standard, such as nodes of start event and end event, providing a consistent model building and communication environment for avionics developers.  
The constraints defined based on SMT were formalized involving complex mathematical theories, providing results in Boolean as returning. These results can help project managers to understand if each work task can satisfy the constraints defined based on the given requirements. Using the KARMA syntax, the process model was built first. Then, costs and days related to cost analysis were defined in a unified formalism. The verification of the satisfaction related to the cost of the avionics system development process was implemented automatically using the SMT solver by defining the cost constraints using the KARMA code. This approach helps stakeholders gain a unified understanding and representation of the process using the graphical notations and enables stakeholders to monitor the satisfaction of plans and objectives when defining processes.  
A hybrid automaton is a finite state machine with discrete jump transitions and continuous variables. The dynamics of the entire development process can be calculated by using the finite state machine that represents a finite number of states and a mathematical model of behavior, such as transitions and actions between those states [36]. In this study, KARMA language was realized to express the group, equation, transition, and other state attributes based on the hybrid automata theory. We defined the cost equations and variable  
\begin{table}
\begin{tabular}{l l c} \hline \hline \multicolumn{3}{c}{**Quantitative Analysis of Models**} \\ \hline
**GOPPRRE** & **Instances** & **Quantity** \\ \hline \multirow{2}{*}{Graph} & The overall development process model of the aircraft avionics system. & \multirow{2}{*}{\(1\)} \\ \cline{2-3} Object & Start event, systems engineering plan, etc. & 33 \\ \hline Relationship & Sequence flow\_1, sequence flow\_2, etc. & 36 \\ \hline Point & none & 0 \\ \hline Role & FlowInput\_1,FlowOutput\_1, etc. & 72 \\ \hline Property & Estimated days, daily cost, etc. & 115 \\ \hline \multirow{2}{*}{Extension (connector)} & connector & \multirow{2}{*}{\(72\)} \\  & (Avionics\_System\_object\_System\_certificate\_review\_d1a3, & \\  & Sequence\_Flow\_2 be8.Sequence\_Flow\_Incoming\_f50f),etc. & \\ \hline \multicolumn{3}{c}{Quantitative analysis of the KARMA script} \\ \hline \multicolumn{3}{c}{Formalized models in KARMA} & 1875 lines \\ \hline \multicolumn{3}{c}{Property verification in KARMA} & 104 lines \\ \hline \multicolumn{3}{c}{Hybrid automata simulation in KARMA} & 138 lines \\ \hline \hline \end{tabular}
\end{table}
Table 6: Quantitative analysis of the case.  
values in the object nodes. In addition, transitions were defined in the relationships, such as day stacking and cost accumulation. Finally, cif solver was used for the simulation. From the simulation results, stakeholders can adjust the task process through the dynamic quantitative data of cost and predict the dynamic performance of cost and time consumption throughout the life cycle.