Abstract:

Coherent systems with binary components have important structural parameters known in literature as signatures and D-spectra. The knowledge of these parameters allows to obtain the probabilistic description of coherent systems behavior in the process of their component failures, and such system characteristics as probabilistic resilience, component importance, system failure probability as a function of component failure probability q, approximations to system reliability, and the bounds on system reliability if we know only the bounds on q.
When the system has many components, the exact calculation of signatures or D-spectra becomes a very complicated issue. We suggest the use for their approximation efficient Monte Carlo procedures. All relevant calculations are illustrated by examples of networks.
This paper provides a nonformal review of relevant literature and the methodology of reliability calculations, based mostly on recently published books and research papers.