## 5 Practical Dependability Assessment
### Experimental Parameter Settings  
The methodology requires some data related to visual nodes, components failure and repair rates, network communication (topology, routing, radio range, etc.) and the application requirements. We assume that all the visual sensor nodes are composed of a camera FLIR BLACKFLY(r)S BFS-U3-13Y3 and that they communicate through an IEEE 802.15.4 radio interface at 2.4 GHz, using a CC2420 antenna which can support WirelessHART setting [31]. Each node is powered by a typical battery of WirelessHART field devices, a lithium battery unit BU 191 [32] and they communicate based on flooding routing strategy. We assume that the useful visual information from cameras can be retrieved of a distance not higher than 75 m from the camera, which implies in a sensing radius of \(R_{s}~{}=~{}75\) m with the viewing angle of \(\theta_{vs}~{}=~{}60^{\circ}\) (an intermediate value and also the average viewing angle of several commercial cameras). Regarding the monitored area, its dimensions are \(w~{}=~{}240\) m and \(h~{}=~{}180\) m, divided into monitoring blocks with \(ws~{}=~{}hs~{}=~{}2.15\) m (approximately 9% of the FoV [22]) and \(\beta\) = 0\({}^{\circ}\). The position of each sensor node was generated according to Figure 10. The dependability parameters, according to the information available in References [33; 34; 32], were pessimistically set, with the hardware failure and repair rates \(\lambda_{htw}~{}=~{}2.2831\times 10^{-5}\) and \(\mu_{htw}\) = 0.0833, respectively, considering the worst case scenario of the hardware components specifications. In this article, all failures, repair and discharging rates are measured by hour. The battery has an initial capacity \(c_{0}~{}=~{}19\) Ah rated by \(H~{}=~{}1\) h and a Peukert's constant \(\eta~{}=~{}1.1\). Considering that the average continuous discharge current needed to supply the sensor node (radio, camera, etc.) is about \(I~{}=~{}150\) mA, then the discharge rates of a 4-discharging stages of the battery model are \(\lambda_{ht0}\) = 0.0225, \(\lambda_{ht1}\) = 0.0197, \(\lambda_{ht2}\) = 0.0187 and \(\lambda_{ht3}\) = 0.0181 h. Once discharged, we consider that it takes 2 hours to repair (replace or recharge) the battery, so \(\mu_{ht}~{}=~{}0.5\). The estimation of the link rates is more complex since the link has a transient behavior, which means that a failed link will reestablish its connection after a while, without an external intervention. A link failure could be caused by an obstruction produced by an external object, shadowing, signal attenuation, multi-path fading, radio interference, background noise, an occupied channel or a data collision [35]. Due to several uncertainties or difficulties when modelling these aspects, usually resulted from a lack of sufficient data, we consider the fuzzy model approach presented in Reference [36] to estimate link failure rates based on link quality metrics. These metrics could be, for instance, packet reception rate, packet error rate (PER), link failure probability or time to link failure (TLF). They can be obtained by simulation [37], estimation [38] or by radio propagation models [39]. Figure 10: Shop floor network. The approach proposed in Reference [36] expresses reliability data (failure probability) in a qualitative natural language and mathematically represented by a membership function of fuzzy numbers. That way, a defuzzification technique is needed to convert the membership function into a reliability score, and later into their corresponding fuzzy failure rates, which is a good approximation for probabilistic failure rates [36]. We use an area defuzzification technique (ADT), since it presented the best results in Reference [36]. Let \(f_{f}=(a,b,c,d)\) be a fuzzy function, where \(a,b,c,d\) are the parameters of a trapezoidal membership function. The parameter \(f_{f}\) can be converted to a crisp score by ADT (Equation (11)) and this score can be used to estimate the link failure rate associated to \(f_{f}\) according to Equation (12).