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August 2000 Reliabilities for feedback systems and their saddlepoint approximation
Ronald W. Butler
Statist. Sci. 15(3): 279-298 (August 2000). DOI: 10.1214/ss/1009212818


It is shown how saddlepoint methods may be used to approximate reliabilities and failure rates of finite stochastic systems with feedback loops. Some countably in .nite state systems including birth-death processes are also considered. The use of saddlepoint methods requires as input the moment generating functions (MGFs) for the system failure time distributions. Some new explicit formulas for these MGFs are given that are amenable to symbolic computation and which also make the numerical computation of saddlepoint approximations quite simple and convenient.


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Ronald W. Butler. "Reliabilities for feedback systems and their saddlepoint approximation." Statist. Sci. 15 (3) 279 - 298, August 2000.


Published: August 2000
First available in Project Euclid: 24 December 2001

zbMATH: 1127.60314
MathSciNet: MR1821330
Digital Object Identifier: 10.1214/ss/1009212818

Keywords: failure rate , Feedback , flowgraphs,reliability , saddlepoint approximation , semi-Markov systems

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.15 • No. 3 • August 2000
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