Current reliability based approaches to structural design are typically element based: they commonly include uncertainties in the structural resistance, applied loads and geometric parameters, and in some cases in the idealized structural model. Nevertheless, the true measure of safety is the structural systems reliability which must consider multiple failure paths, load sharing and load redistribution after member failures, and is beyond the domain of element reliability analysis. Identification of system failure is often subjective, and a crisp definition of system failure arises naturally only in a few idealized instances equally important. We analyse the multi-girder steel highway bridge as a 𝑘 out of 𝑛 active parallel system. System failure is defined as gross inelastic deformation of the bridge deck; the subjectivity in the failure criterion is accounted for by generalizing 𝑘 as a random variable. Randomness in 𝑘 arises from a non-unique relation between number of failed girders and maximum deflection and from randomness in the definition of the failure deflection. We show how uncertain failure criteria and structural systems analyses can be decoupled. Randomness in the transverse location of trucks is considered and elastic perfectly plastic material response is assumed. The role of the system factor modifying the element-reliability based design equation to achieve a target system reliability is also demonstrated.