Correspondingly system failure represents the situation where the event of failure involves
several failure modes, either as a possibility or as a necessity. In Figure 9.1b) the possible
collapse failure modes are illustrated for the frame structure where bending failure modes
have been assumed for the individual cross sections of the frame.
In the subsequent some of the most important aspects of systems reliability analysis will be
considered, namely first the probabilistic characteristics of systems in general and thereafter
aspects of the mechanical modelling of structural systems. The emphasis will be directed to
the basic features and the modelling of systems. Advanced methods for the calculation of
failure probabilities of systems are not addressed in the present text as such methods may be
considered standardised tools available in several commercial software packages.
9.2 Probabilistic Characteristics of Systems
In the same way logical systems such as fault trees and event trees are used for the systematic
analysis of the reliability of technical systems, block diagrams are normally used for the
representation of systems in the reliability analysis of structural systems. In Figure 9.2 typical
block diagrams are shown. The components of the systems represent failure events of the
individual failure modes involved in the systems failure event.
Figure 9.2: Block diagrams used in the reliability analysis of structural systems.
In Figure 9.2a) a series system is illustrated which may be used to represent the failure of
structural systems failing if any of the failure modes of the structural system fails. In Figure
9.2b) a parallel system is illustrated which may be used to represent the failure of a structural
system, which fail only if all of the failure modes of the structural system fail. Finally in
Figure 9.2c) a series system of parallel systems is illustrated which may be used to represent
the failure of a structural system, which fails if any of the sub-systems (parallel systems)
representing failure of several failure modes fail.