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Non-Parametric Estimators Related to Local Load-Sharing Models
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
1999 (English)Report (Other academic)
Abstract [en]

We consider the problem of estimating the cumulative distribution function of failure stresses of bundles (i.e. the tensile forces that destroy bundles), constructed of several statistically similar fibres, given a particu-lar kind of censored data. Each bundle consists of several fibres which have their own independent identically distributed failure stresses, and where the force applied on a bundle at any moment is distributed between the fibres in the bundle according to the local load-sharing model.

The testing of several bundles generates a special kind of censored data, which is complexly structured. Consistent non-parametric estima-tors of the distribution laws of bundles are obtained by applying the theory of martingales, and by using the observed data. It is showed that ran-dom sampling, with replacement from the statistical data related to each tested bundle, can be used to estimate the accuracy of our non-parametric estimators. Numerical examples illustrate the behavior of the obtained es-timators.

Place, publisher, year, edition, pages
1999.
Series
Research report in mathematical statistics, ISSN 1653-0829
Keyword [en]
Non-parametric estimation, Load-sharing models, Local load-sharing models, martingale, resampling, life testing, reliability
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-46728OAI: oai:DiVA.org:umu-46728DiVA: diva2:440238
Available from: 2011-09-12 Created: 2011-09-12 Last updated: 2011-09-15Bibliographically approved
In thesis
1. Statistical analysis and simulation methods related to load-sharing models.
Open this publication in new window or tab >>Statistical analysis and simulation methods related to load-sharing models.
2000 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

We consider the problem of estimating the reliability of bundles constructed of several fibres, given a particular kind of censored data. The bundles consist of several fibres which have their own independent identically dis-tributed failure stresses (i.e.the forces that destroy the fibres). The force applied to a bundle is distributed between the fibres in the bundle, accord-ing to a load-sharing model. A bundle with these properties is an example of a load-sharing system. Ropes constructed of twisted threads, compos-ite materials constructed of parallel carbon fibres, and suspension cables constructed of steel wires are all examples of load-sharing systems. In par-ticular, we consider bundles where load-sharing is described by either the Equal load-sharing model or the more general Local load-sharing model.

In order to estimate the cumulative distribution function of failure stresses of bundles, we need some observed data. This data is obtained either by testing bundles or by testing individual fibres. In this thesis, we develop several theoretical testing methods for both fibres and bundles, and related methods of statistical inference.

Non-parametric and parametric estimators of the cumulative distribu-tion functions of failure stresses of fibres and bundles are obtained from different kinds of observed data. It is proved that most of these estimators are consistent, and that some are strongly consistent estimators. We show that resampling, in this case random sampling with replacement from sta-tistically independent portions of data, can be used to assess the accuracy of these estimators. Several numerical examples illustrate the behavior of the obtained estimators. These examples suggest that the obtained estimators usually perform well when the number of observations is moderate.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2000. 29 p.
Keyword
Non-parametric and parametric estimation, load-sharing models, asymptotic distribution, martingale, resampling, life testing, reliability
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-46772 (URN)91-7191-965-1 (ISBN)
Public defence
2001-02-02, MA 121, Umeå University, 14:03 (English)
Opponent
Supervisors
Available from: 2011-09-15 Created: 2011-09-13 Last updated: 2011-09-15Bibliographically approved

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Citation style
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