Inferences for the fatigue life model based on the Birnbaum-Saunders distribution

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13 Citations (Scopus)

Abstract

Time to fracture from cracks in materials under fluctuating stress is often well approximated by the Birnbaum-Saunders (BISA) distribution. Unlike the Weibull and lognormal model, there is not much research on the accuracy of the parameter estimation on the BISA distribution under Type I (time) censoring. This article explores and compares different procedures to compute confidence intervals for parameters and quantiles of the BISA distribution for complete and Type I censored data. The procedures are based on using maximum likelihood estimators and can be classified into three groups as the commonly-used normal-approximation, the likelihood ratio, and the parametric bootstrap procedures. The procedures in all three groups are justified on the basis of large-sample asymptotic theory. We use Monte Carlo simulation to investigate the finite sample properties of these procedures and give suggestions of which procedure to use according to proportion failing and number of failures.

Original languageEnglish
Pages (from-to)43-60
Number of pages18
JournalCommunications in Statistics Part B: Simulation and Computation
Volume32
Issue number1
DOIs
Publication statusPublished - 2003 Feb 1

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Birnbaum-Saunders Distribution
Fatigue Life
Parameter estimation
Maximum likelihood
Fatigue of materials
Model-based
Cracks
Large Sample Theory
Parametric Bootstrap
Normal Approximation
Weibull
Censored Data
Likelihood Ratio
Asymptotic Theory
Censoring
Quantile
Maximum Likelihood Estimator
Confidence interval
Parameter Estimation
Monte Carlo simulation

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Statistics and Probability

Cite this

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title = "Inferences for the fatigue life model based on the Birnbaum-Saunders distribution",
abstract = "Time to fracture from cracks in materials under fluctuating stress is often well approximated by the Birnbaum-Saunders (BISA) distribution. Unlike the Weibull and lognormal model, there is not much research on the accuracy of the parameter estimation on the BISA distribution under Type I (time) censoring. This article explores and compares different procedures to compute confidence intervals for parameters and quantiles of the BISA distribution for complete and Type I censored data. The procedures are based on using maximum likelihood estimators and can be classified into three groups as the commonly-used normal-approximation, the likelihood ratio, and the parametric bootstrap procedures. The procedures in all three groups are justified on the basis of large-sample asymptotic theory. We use Monte Carlo simulation to investigate the finite sample properties of these procedures and give suggestions of which procedure to use according to proportion failing and number of failures.",
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