Accuracy of approximate confidence bounds computed from interval censored weibull and lognormal data

Interval censored data arise frequently in industrial life tests and other applications. Maximum likelihood estimation provides a convenient means for making inferences on important distribution properties like quantiles and failure probabilities. The asymptotic normal distribution of the maximum likelihood estimators provides a simple method of setting approximate confidence bounds on these quantiles. Inverting likelihood ratio tests is another alternative. This paper uses Monte Carlo Simulation to investigate the finite sample properties of maximum likelihood estimators of Weibull and lognormal parameters and quantiles from interval censored data. We evaluate the accuracy of large sample one- and two-sided confidence bounds based on asymptotic normal theory and compare their accuracy (with respect to coverage probability) to those obtained by inverting likelihood ratio tests. Even though these procedures are asymptotically equivalent, our results show that the intervals based on inverting a likelihood ratio test generally have coverage properties that are closer to the nominal confidence levels.