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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.'', pp. 2201.</ref>
<math> \mathbf R</math>
== References ==
{{reflist}}
== Bibliography ==
* Beck, André T.; Melchers, Robert E., "Fatigue and fracture reliability analysis under random loading", pp. 2201–2204 in, Bathe, K.J (ed), ''Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics'' June 17–20, 2003, Elsevier, 2003 {{ISBN|008052947X}}.
* Murthy, Pappu L.N.; Mital, Subodh K.; Shah, Ashwin R., "Design tool developed for probabilistic modeling of ceramic matrix composite strength", [https://books.google.co.uk/books?id=Q9eAxUlA4x0C&pg=PA127 pp. 127–128] in, ''Research & Technology 1998'', NASA Lewis Research Center, 1999.
* Shah, A.R.; Shiao, M.C.; Nagpal, V.K.; Chamis, C.C., [https://books.google.co.uk/books?id=oag3AQAAMAAJ ''Probabilistic Evaluation of Uncertainties and Risks in Aerospace Components''], NASA Technical Memorandum 105603, March 1992.
* Wen, Y.K.; Chen, H.C., [https://www.sciencedirect.com/science/article/abs/pii/0266892087900063 "On fast integration for time variant structural reliability"], ''Probabalistic Engineering Mechanics'', vol 2, iss. 3, pp. 156-162, September 1987.
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