# Gaining Insights into Conceptual Models: A Graph-Theoretic Querying Approach
## 5 Use Cases for OPM Queries
### Cause and Effect in Model-Based System Engineering
#### 5.1.2 Possible Causes by Backward Chaining: The Case of the Three Mile Island Nuclear Accident  
The accident in the second reactor of TMI-2 was caused due to many reasons, which started eleven hours before the meltdown. To demonstrate the OPM query capability, we focus on the **Pilot Operated Relief Valve (PORV)** component in the steam generating subsystem. According to the TMI control room operators' understanding, there were only two states that the **PORV** can be at: **closed** or **open**. The same is true for the instruments of the control room, which indicate only if the **PORV** is **open** or **closed**. The post-incident review of this accident shows that the **PORV** was in a \"**stuck-open**\" state--a state that had never before been considered as possible. The operators were not aware of the cooling water pouring out through the **stuck-open PORV**. Because of that, the operators did not identify the loss of coolant accident that caused the core to overheat and initiated the nuclear fuel pellets' cladding to rupture, eventually leading to core melting. Figure 8: Neighborhood OPM query result of an airplane collision avoidance model. A fault-aware model, described in [38] as the second version of implementing the \"Cyber Physical Gap Aware Modeling and Engineering\" (CPGAME), is a model that enhances the original one with potential faults of each component. The second of the three model versions describes only the physical failures and system identification for those failures. Designers and engineers usually avoid this kind of modeling, as it involves failed component states, putting in question its reliability. In our case, the \"melted\" state of the reactor core was not considered. Figure 9 shows the process **Steam Generating** in-zoomed with the related objects, including the process **Meltdown**, which changes the state of the stateful object **Reactor Core** from its initial state **cooled** to **melted**. Mitigation of such accidents could be achieved by reviewing all the processes, objects, and object states of the failure aware OPM model, and following the chain of events that leads to a change in the system's health into an instable or even a disastrous state, as modeled in Figure 9. We execute the Directional query within the Neighborhood OPM Queries, placing the state **melted** of the **Reactor Core** object as the graph's root node and specifying \"Incoming\" for the \"Direction\" property of the \"Neighborhood Queries\" (see Section 6.2), thus asking for all the incoming links. The query result in Figure 10 shows all the elements that contributed to the meltdown as part of the **Steam Generating** process. The **PORV** at state **Stuck Open** and **Core Water Level** at state **too low** are the failure-aware elements that trigger the processes that eventually caused the accident of the nuclear fuel pellet meltdown. This OPM model was generated postmortem, so it focuses on the physical failure that caused the meltdown. Modeling a system with as many as possible failure modes and undesired states, along with possible ways to avoid them, such as adding more  
Figure 9: OPD of the fault-aware **Steam Generating** process in-zoomed. sensors and polling them where it is known that the actual state is critical, is bound to yield an OPM model that is much more complex than the current one. This is where the ability to query the OPM model becomes of paramount importance, as it helps focusing on analysis of possible failures and the contribution of additional components to the mitigation of those failures, ensuring that the system is made more reliable and robust. Classical shortest-path algorithms [39], including the class of travelling salesman problems, commonly used for network routing problems, are challenging classical combinatorial optimization problems [40; 41]. A shortest-path query on conceptual models can reveal the path that requires the minimal effort or cost, for example by following weighted edges that contribute the least to the total of the objective parameter.