When the robustness of a public service system design is tested, we can often use scenarios where possible random failures can occur and they can influence the time the service is accessible which is provided for system users. The construction of a suitable scenario is based on the choice of links of the transportation network which influence the system performance in a substantial way. In such scenarios one or multiple arcs can be affected by this failure. In our contribution we present characteristics of pairs of critical arcs that can be used to develop an algorithm for the creation of critical scenarios.