Bootstrap Confidence Interval for the Median Failure Time of Three-Parameter Weibull Distribution

In many applications of failure time data analysis, it is important to perform inferences about the median of the distribution function in situations of failure time data modeling with skewed distribution. For failure time distributions where the median of the distribution function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can be obtained. However, these results might not be very accurate for small sample sizes and/or with large proportion of censored observations. Considering the three-parameter Weibull distribution for the failure time data, we present and compare the accuracy of asymptotical confidence intervals with confidence intervals based on bootstrap simulation. The alternative methodology of confidence intervals for the median of the three-parameter Weibull distribution function is illustrated by using real data from engineering field. The nonparametric bootstrap procedure was implemented in the SAS® system which incorporated proc nlp, proc surveyselect and proc iml in the SAS® macro environment.