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On the estimation of failure probability having prescribed statistical moments of first passage time
Authors:B.F. Spencer Jr.  L.A. Bergman
Affiliation:1. Plant Breeding and Genetics Section, School of Integrative Plant Science, Cornell University, Ithaca, NY 14853, USA;2. Robert W. Holley Center for Agriculture and Health, USDA-Agricultural Research Service, Cornell University, Ithaca, NY 14853, USA;3. State Key Laboratory of Crop Genetics & Germplasm Enhancement, Nanjing Agricultural University, Nanjing 210095, China;4. Key Laboratory of Horticultural Plant Biology (Ministry of Education), Huazhong Agricultural University, Wuhan 430070, China;5. Department of Vegetable Research, ARO, Newe Ya''ar Research Center, P.O. Box 1021, Ramat Yishay 30095, Israel
Abstract:A method of estimating the probability density function and cumulative distribution function when only the ordinary or central moments of the distribution are known is examined. The technique is used in conjunction with previous work which yields the ordinary moments of time to first passage failure to obtain accurate estimates of the failure probability for two representative oscillators. The results are then compared to those obtained by a nearly exact numerical scheme.
Keywords:first passage failure   maximum entropy   reliability   probability density function   cummulative distribution function   statistical moments   random vibration
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