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October, 1968 On Confidence Limits for the Reliability of Systems
Janet M. Myhre, Sam C. Saunders
Ann. Math. Statist. 39(5): 1463-1472 (October, 1968). DOI: 10.1214/aoms/1177698125


The asymptotic chi-square distribution of the log-likelihood ratio is used to obtain approximate confidence intervals for the reliability of any system which may be represented by a monotone function of Bernoulli variates. This generalizes the results of A. Madansky, Technometrics, November 1965, for series, parallel and series-parallel systems. The method used is to parameterize the log-likelihood equation so as to find the interval of parameter values which keeps the log-likelihood less than or equal to the specified quantile of the chi-square distribution. This is done by introducing an operator depending upon the parameter, a fixed point of which is the solution of the likelihood ratio equation, and by showing the operator is a contractive map and hence has a unique fixed point depending continuously on the parameter. The solution can be found simply by iteration.


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Janet M. Myhre. Sam C. Saunders. "On Confidence Limits for the Reliability of Systems." Ann. Math. Statist. 39 (5) 1463 - 1472, October, 1968.


Published: October, 1968
First available in Project Euclid: 27 April 2007

zbMATH: 0193.17801
MathSciNet: MR232517
Digital Object Identifier: 10.1214/aoms/1177698125

Rights: Copyright © 1968 Institute of Mathematical Statistics

Vol.39 • No. 5 • October, 1968
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