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Line 5: If failure barrier crossings are assumed to comply with the [[Poisson counting process]] an expression for maximum probable failure can be developed for each stress variable. The overall probability of failure is obtained by averaging (that is, [[integral\|integrating]]) over the entire variable vector space. FPI is a method of approximating this integral. The input to FPI is a time-variant expression, but the output is time-invariant, allowing it to be solved by [[first-order reliability method]] (FORM) or second-order reliability method (SORM).<ref>Beck & Melchers, p. 2201.</ref> An FPI package is included as part of the core modules of the [[NASA]]-designed [[NESSUS Probabilistic Analysis Software\|NESSUS]] software.<ref>Shah ''et al.'', p. 5.</ref> It was initially used to analyse risks and uncertainties concerning the [[Space Shuttle main engine]],<ref>Shah ''et al.'', p. 5.</ref> but is now used much more widely in a variety of industries.<ref>Riha ''et al.'', ppp. 53.</ref> == References ==

Fast probability integration: Difference between revisions