Fast probability integration: Difference between revisions

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'''Fast probability integration''' ('''FPI''') is a method of determining the probability of a class of events, particularly a failure event, that is faster to execute than [[Monte Carlo analysis]].<ref>Pappu ''et al.'', p. 128.</ref> It is used where large numbers of time-variant variables contribute to the reliability of a system. The method was proposed by Wen and Chen in 1987.<ref>Beck ''et al.'', ppp. 2201.</ref>

For a simple failure analysis with one stress variable, there will be a time-variant failure barrier, <math>r(t)</math>, beyond which the system will fail. This simple case may have a deterministic solution, but for more complex systems, such as crack analysis of a large structure, there can be a very large number of variables, for instance, because of the large number of ways a crack can propagate. In many cases, it is infeasible to produce a deterministic solution even when the individual variables are all individually deterministic. In this case, one defines a probabilistic failure barrier surface, <math> \mathbf R (t)</math>, over the [[vector space]] of the stress variables.

<math> \mathbf R</math>

== References ==