# Improving the Functional Reliability of an Urban Public Transport Line
## 2 Materials and Methods
### Functional Reliability of Urban Public Transport Network Services
Under these conditions, functional reliability is defined as the ability of the service network to keep its effectiveness above the critical level, a property to which an appropriate probabilistic indicator can be associated. For example, for the functional reliability of the service of an urban public transportation network, a metric/indicator \(\alpha\) can be considered and probabilistically defined by the relation  
\[\alpha=P(E\geq E_{C}) \tag{2}\]  
where \(E_{C}\) is the critical value of the effectiveness indicator, \(E\)--current value of the effectiveness indicator, which is influenced by the defects during the operation of the services' network. For example, if this objective is that of sustainable mobility, i.e., that of attracting as many users as possible to public transportation, the indicator of effectiveness could be defined by the average loading degree (calculated as the total number of passengers \(\times\) km divided by the total offered capacity of transport \(\times\) km). However, the total number of actual circulated passengers \(\times\) km is difficult to register without specific equipment on terms, or in tram stops. That is why using one or another functional reliability function needs a careful decision on the adopted metric. Anyway, the choice of the most suitable functional reliability indicator (\(X\) or \(E\)) must consider simplicity, stability in a statistical sense, and its importance in defining the system's functionality. In any of the two ways of defining the functional reliability of the transportation network services, it is obvious that there is a direct link between the functional reliability and the quality of mobility for individual journeys, respectively, for public transportation of different types. Regarding the calculation of the reliability indicators for the physical network components (infrastructure, means of transport, equipment), there are no methodological difficulties [26; 27]. On the contrary, regarding the functional reliability of the services' network (which includes the planned operating technology/method for service adaptation to the size of the estimated demand as well as to the multitude of endogenous and exogenous disruptive phenomena producing deviations from the planned offer), the difficulties are major. Defining one of the mentioned indicators (\(X\) or \(E\)) of the functional reliability of the transportation services' network, the evaluation must be based on the types of technological disturbances and the correct estimation of their consequences. Technological irregularities in the operation of the services' network mean complex events that cause deviations (discontinuities) in the programmed sequence of operations that ensure the continuity and stability of the entire process. In the case of the occurrence of these technological irregularities, in addition to the causes attributed to the technical elements (e.g., breakdowns, insufficient capacities for transport demand at rush hours, lack of correlations between the capacities of the subsystems, etc. ), exogenous causes (coming from the natural environment or riparian man-made systems, etc.) must also be taken into account, as well as consequences of some non-compliant actions of the operators involved (due to imprecision, insufficiency or lack of information, information overload, insufficient time for the elaboration of management decisions, non-compliance with the regulations related to a certain department, etc.). We consider functional reliability as a defining characteristic in user assessment/perception of the performance of a public transportation service network. We appreciate that there is no need to assign a norm/standard value of functional reliability, as generally valid for any public transport network. This is because functional reliability varies by project, location, user, reason for travel, and time.