The Annals of Mathematical Statistics

On Confidence Limits for the Reliability of Systems

Janet M. Myhre and Sam C. Saunders

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Math. Statist., Volume 39, Number 5 (1968), 1463-1472.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177698125

Digital Object Identifier
doi:10.1214/aoms/1177698125

Mathematical Reviews number (MathSciNet)
MR232517

Zentralblatt MATH identifier
0193.17801

JSTOR
links.jstor.org

Citation

Myhre, Janet M.; Saunders, Sam C. On Confidence Limits for the Reliability of Systems. Ann. Math. Statist. 39 (1968), no. 5, 1463--1472. doi:10.1214/aoms/1177698125. https://projecteuclid.org/euclid.aoms/1177698125


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