On Non-Parametric Estimation of Poission Point Processes Related to Failure Stresses of Fibres

• We consider statistical analysis of the reliability of fibres. The problem is to estimate the distribution law of random failure stresses of fibres (i.e. the critical level of stresses that destroy fibres) by using data obtained in a special kind of test, where several fibres are tested until they break. All new pieces resulting from this test will also be tested, if they are long enough. The test ends when all the remaining pieces are too short to be tested further. We refer to these as binary tree structured tests. We assume that the cumulative hazard function (c.h.f.) of the failure stresses of these fibres is continuous, and that the fibres are statistically identical. Under these assumptions we obtain, as the number of tested fibres increases, a strongly consistent Nelson-Aalen type estimator of the c.h.f. The functional central limit resampling theorem in Skorohod space is proved. It justifies the possibility of using resampling for estimating the accuracy of these estimators. The theorem shows that resampling can be used to asymptotically consistently estimate distribution laws of continuous functionals of the random deviations between the estimator and the true c.h.f.. For example, resampling can be used to estimate the distribution law of the maximum distance between estimators and estimands. Numerical examples suggest that resampling works well for a moderate number of tested fibres.

Ämnesord

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

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

Nyckelord

load-sharing models

non-parametric esti-mation

binary tree structured tests

resampling

reliability

martingale

Skorohod space

Mathematical statistics

Matematisk statistik

Publikations- och innehållstyp

vet (ämneskategori)

rap (ämneskategori)