## 5 Methodology for Reliability and Availability Evaluation
### Assumptions  
The main assumptions considered in the methodology are the following:  
* **Topology:** the network is composed of \(N\) field devices, which can belong to one of the following types: end device (e.g., sensor/actuator node), router, access point and gateway (_i.e._, sink). Devices are arranged according to one of the following topologies: line, star, cluster and mesh. These elements are defined according to the WirelessHART, ISA 100.11a and Zigbee standards;
* **Faults:** only permanent faults are considered. The links, due to its wireless nature, are only affected by transient faults and thus are considered to be reliable (_i.e._, they do not fail). Thus, only field devices can fail. After a permanent fault a device is considered failed (permanently). We assume that device failures are independent. In principle any type of distribution can be used to characterize the occurrence of device failures. However, the sharpe tool poses some restrictions. The tool imposes that CDFs must be expressed using _exponential polynomial_ terms as following \[F(t)=\sum_{j=1}^{n}a_{j}t^{k_{j}}e^{b_{j}t}\] (11) Many distributions can be expressed in this way (e.g., exponential, Erlang, hypoexponential, hyperexponential). Other distributions (e.g., Weibull, deterministic) can be approximated using exponential polynomial terms. Further details can be found in [46].
* **Repairs:** field devices can be repaired after failing, if necessary. After a repair the device is considered as new. We consider that repair processes are independent and that the number of repairman (_i.e._, number of repair actions) is not limited. The time necessary to repair a device is characterized by a _repair distribution_. This distribution is defined in analogous way to the failure distribution discussed previously;  
Figure 4: Overview of the methodology for reliability and availability evaluation.  
* **Redundancy:** field devices can have an internal redundant architecture with several available spares. We assume that when the main element fails, its replacement by a spare is always performed with success;
* **Reconfiguration:** when a device fails the network topology can change. We assume that the network manager (WirelessHART) or system manager (ISA 100.11a) is able to identify with success a device failure, and then update the network topology (communication paths). It is also assumed that the time required to perform this operation is negligible and that it is always successful (if alternative paths exist). Thus, the support of self-healing routing protocols is assured, since all paths between a field device and the gateway are considered;
* **Measures:** the following measures can be computed: reliability, unreliability, availability, unavailability, MTTF and component importance (Birnbaum and Criticality). Results can be presented both numerically and symbolically using exponential polynomial terms.
* **Inputs:** to compute the measures it is necessary to provide the following input data: network topology, type of devices, device's redundancy, network failure condition, characteristics of the device's failure and repair processes and measures to compute.