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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