Non-Parametric Estimators Related to Local Load-Sharing Models

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Non-parametric estimation

Load-sharing models

Local load-sharing models

martingale

resampling

life testing

reliability

Publication and Content Type

vet (subject category)

rap (subject category)