Reliability Bounds for Multicriteria Systems

This paper deals with general structure functions, where arbitrary degrees of performance between perfect functioning and complete failure are allowed for each component and the n-component system itself. We make the assumption that the n-component system can be modelled as a structure function given by a mapping φ:L ⁿ →L ^k ₀, L and L₀ being two linearly ordered sets, so that the performance of the system is evaluated according to k single criteria. Global concepts of minimal path and minimal cut are discussed for these multicriteria systems; general reliability bounds based on them are deduced and compared with those given in previous papers.