umu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Estimation of the reliability of systems described by the Daniels Load-Sharing Model
Umeå University, Faculty of Science and Technology, Mathematical statistics. (Matematical Statistics)
1999 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 1999.
Keyword [en]
Non-parametric and parametric estimation, Equal Load-sharing models, asymptotic distribution, martingale, resam-pling, life testing, reliability
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-46724OAI: oai:DiVA.org:umu-46724DiVA: diva2:440224
Available from: 2011-09-13 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

Open Access in DiVA

fulltext(35786 kB)143 downloads
File information
File name FULLTEXT01.pdfFile size 35786 kBChecksum SHA-512
1f6b4a5fde76d3140bec89cbc9180558c70945fdcc6a4cf4e3d36555fa2fa2ae28ba9fddf7a150c985b7d5a968360ede09a3c9248cb64bfa046db53612ec229b
Type fulltextMimetype application/pdf

Authority records BETA

Rydén, Patrik

Search in DiVA

By author/editor
Rydén, Patrik
By organisation
Mathematical statistics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 143 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 107 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf