# Automated Methodology for Dependability Evaluation of Wireless Visual Sensor Networks
## 3 Problem Formulation and Background
### Integration of Models  
In this section, we present how to integrate hardware, battery and link models (with the strategies of routing protocols) in order to obtain a single system model. As aforementioned, the WVSN scenario considered in this paper and presented in Figure 1 is affected by different classes of failures. Coverage failures are the most important in a WVSN, and they are related to the inability of essential visual nodes to deliver their information to the sink. An essential node is one that directly participates on the required monitoring, so it determines the network failure condition (NFC). The NFC of a WVSN application consists of a logical expression that represents the combinations of components that, if failed, lead to the application failure [6]. Since we are considering WVSNs for area coverage, these combinations must be composed by essential visual nodes. Without the visual information from these nodes, the visual information gathered by the rest of the network is not enough to compose the required minimum area to be monitored [14]. For example, analyzing Figure 1, it is possible to notice that node \(V1\) monitors a small area (rectangle) and the majority of this area is also monitored by nodes \(V2\) and \(V3\). Node \(V2\) monitors a larger area than \(V1\), but also with some overlapping related to \(V1\) and \(V3\). That way, the NFC for this network should probably be \(NFC=V2\lor V3\), depending on the application requirements. This failure condition is assessed _true_ if \(V2\) is assessed _true_ (if the hardware of \(V2\) fails) or if \(V3\) is assessed _true_ (if the hardware of \(V3\) fails), indicating that the nodes \(V2\) and \(V3\) are essentials for visual monitoring. In this case, if at least one of these nodes fails, then the remaining visual nodes are not able to collect enough visual information to meet the application requirements. On the other hand, the application could require a minimum area slightly larger than the coverage area of any visual sensor, it being necessary that at least two visual nodes are able to deliver their visual information to the sink in order to fulfill the application requirements. In other words, if any combination of two visual nodes fail, the application will fail, which implies \(NFC=(V1\wedge V2)\lor(V1\wedge V3)\lor(V2\wedge V3)\). However, visual information of an essential node may also not reach the sink due to communication failures. For instance, if the node \(S2\) fails, then there will be no way to deliver the visual information from both nodes \(V1\) and \(V2\). In the same way, if the link connecting nodes \(S1\) and \(S2\) fails, or if the link connecting nodes \(V2\) and \(S2\) fails, then there will be no way to deliver the visual information from both nodes \(V1\) and \(V2\), respectively. Those elements must appear in the evaluation of the whole system since they indirectly affect its dependability. To cope with these issues, we model the system using Fault Trees (FT), similarly to [PERSON] et al. [6] and [PERSON] et al. [14], considering the previous classes of failures. A Fault Tree is a graphical procedure  
Figure 8: Routing strategies: (**a**) direct and (**b**) flooding. used to describe the combination of events that leads to a TOP event, in a treelike structure composed by events and logic gates [6]. In this case, the logic gates are used to represent cause-effect relationships among events, in an equivalent sense of the NFC. That way, the NFC is defined by a logical expression, composed by AND and OR gates, and has to be evaluated as _true_ to identify an application failure. An AND gate indicates that a failure condition occurs if, and only if, all input events has occurred. In the OR gate case, the failure condition occurs if at least one input event has occurred [6; 56]. The inputs of these gates are either single events or combinations of events which result from the output of other gates.