This paper compares different procedures to compute confidence intervals for parameters and quantiles of the Weibull distribution for Type I censored data from life test experiment. The methods can be classified into three groups. The first group contains methods based on the commonly-used normal approximation for the distribution of (possibly transformed) studentized maximum likelihood estimators. The second group contains methods based on the likelihood ratio statistic and its modifications. The methods in the third group use a parametric bootstrap approach, including the use of bootstrap-type simulation to calibrate the procedures in the first two groups. All of these procedures are justified on the basis of large-sample asymptotic theory. We use the Monte Carlo simulation to investigate the finite sample properties of these procedures. Our results show that the coverage probability of one-sided confidence bounds is much worse than those of two-sided confidence intervals calculated from methods in the first and second group. Usual normal-approximation methods are crude unless the expected number of failures is large (>50 or 100). The likelihood ratio methods work much better and provide an adequate procedure down to 30 or 20 failures. The second-order bootstrap procedures do not perform equally well in small samples. By using bootstrap methods with caution, the coverage probability is close to nominal for expected number of failures down to 15 or less and even down to 10 or less for lightly censored cases (proportion failing > 50%). Exceptional cases, which are due to problems caused by the Type I censoring, are noted.

Keywords: Bartlett correction, bias-corrected accelerated bootstrap, bootstrap-t, life data, likelihood ratio, ML estimator, parametric bootstrap, Type I censoring.
 

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