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Estimation of the reliability of systems described by the Daniels Load-Sharing Model [Elektronisk resurs]

Rydén, Patrik (författare)
Matematical Statistics (medarbetare)
Umeå universitet Teknisk-naturvetenskapliga fakulteten (utgivare)
Publicerad: Umeå : Umeå universitet, 1999
Engelska.
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  • E-bokAvhandling(Lic.-avh. Umeå : Umeå universitet, 1999)
Sammanfattning Ämnesord
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  • We consider the problem of estimating the failure stresses of bundles (i.e. the tensile forces that destroy the bundles), constructed of several statisti-cally similar fibres, given a particular kind of censored data. Each bundle consists of several fibres which have their own independent identically dis-tributed failure stresses, and where the force applied on a bundle at any moment is distributed equally between the unbroken fibres in the bundle. A bundle with these properties is an example of an equal load-sharing sys-tem, often referred to as the Daniels failure model. The testing of several bundles generates a special kind of censored data, which is complexly struc-tured. Strongly consistent non-parametric estimators of the distribution laws of bundles are obtained by applying the theory of martingales, and by using the observed data. It is proved that random sampling, with replace-ment from the statistical data related to each tested bundle, can be used to obtain asymptotically correct estimators for the distribution functions of deviations of non-parametric estimators from true values. In the case when the failure stresses of the fibres are described by a Weibull distribution, we obtain strongly consistent parametric maximum likelihood estimators of the distribution functions of failure stresses of bundles, by using the complexly structured data. Numerical examples illustrate the behavior of the obtained estimators. 

Ämnesord

Natural Sciences  (hsv)
Mathematics  (hsv)
Probability Theory and Statistics  (hsv)
Naturvetenskap  (hsv)
Matematik  (hsv)
Sannolikhetsteori och statistik  (hsv)
MATHEMATICS  (svep)
Applied mathematics  (svep)
Mathematical statistics  (svep)
MATEMATIK  (svep)
Tillämpad matematik  (svep)
Matematisk statistik  (svep)

Indexterm och SAB-rubrik

Non-parametric and parametric estimation
Equal Load-sharing models
asymptotic distribution
martingale
resam-pling
life testing
reliability
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