# Improving the Functional Reliability of an Urban Public Transport Line
## 2 Materials and Methods  
### Functional Reliability of Urban Public Transport Network Services  
The reliability of public, commercial, technological, or touristic transport, but also that of individual car trips, to a certain extent, stands out as one of the primary factors that determine the levels reached in the quality of transport or traffic. Related to the quality of public transport, the reliability of the network cannot be limited to the reliability of the physical network/support. It means that the definition of the reliability of a product, or the reliability of the traffic/transport networks, does not sufficiently reflect the quality of the service provided by the network. A public transport network with extremely good reliability of the underlying physical network (expressed by a probability tending to the maximum value) is not equivalent to a service network with similar reliability. The reliability of the service implies another way of definition, related to the performance of the operation as users perceive it. The reliability of the service is conditioned not only by the reliability of the physical network but is defined by the probability of maintaining connectivity between two network points. It is also conditioned by the reliability of means of transport, control, and command equipment, but also by the actions of human operators involved in the development of traffic. The technologies adopted to ensure the stability and continuity of movement contained in the presentation quality of the offered service (in terms of reliability) summarize the reliability of the above components. It follows that in the case of the service network, another definition of reliability must be used, more comprehensive, and as consistent as possible with how it is reflected in the quality of services provided by the traffic network, i.e., functional reliability [14], as a benchmark of the attractiveness of the offered service. As a result, it is necessary to return to a broader understanding of the notion of reliability. This needs to be understood as the ability of the system to ensure the success of the entrusted mission. We note certain difficulties in defining the functional reliability of the service network by reference to \"mission success\". Specifying the \"success of the mission\" requires a collaboration between the public authority, the infrastructure manager, the user, the designer, and, possibly, a specialized third institution (e.g., a quality certification entity). Divergent points of view are required to be harmonized, referring to the preliminary specifications of the public authority, the operator, the user, and the information on the services provided by similar competing networks (if any). As a result, two ways of defining reliability for transportation service networks are possible. The first one reduces the mission of the network service to the keeping/preserving of certain parameters or functional characteristics (e.g., compliance with traffic schedule, comfort, duration, technical efficiency, commercial efficiency, etc.) within certain specified boundaries. Under these conditions, functional reliability represents the probability that the service network will preserve its functional indicators/indices/metrics during a given time interval, within certain boundaries. \[P(S)=P(X_{1}\leq X\leq X_{2}) \tag{1}\]  
where \(P(S)\) is the probability of mission success \(S\), which means maintaining the functional metrics \(X\) inside the range of boundaries; \(X\)--a random value representing the operational indicators/indices/metrics of the system; \(X_{1},\ X_{2}\)--accepted boundaries of random indicators \(X\). The second way is related to the effectiveness of the system. The occurrence of \"defects\" in the system has the main effect of worsening the effectiveness indicator, whose value could fall below a certain critical value (which is set according to the purpose pursued).