Some properties of maximum likelihood estimators of Weibull parameters with Type I censored data. - Hannah K Finselbach (2007)
This thesis looks at extending previous work in the field of Type I censored reliability experiments. Due to its popularity and wide use, we use the Weibull distribution, and provide formulae on asymptotically valid variances and covariance of the maximum likelihood estimates and quantiles. We also examine the effect that sample size and censoring levels have on such properties. Theoretical results are validated with simulation studies throughout. These results are then used to obtain measures of precision in the Weibull parameter and quantile estimates given the assumption of asymptotic Normality. The suitability of using this large sample Normal theory in finite samples is consequently studied, and we provide an alternative measure of precision using relative likelihood methods. Confidence regions for each method are compared using published data. We investigate the concept of undertaking interim analysis of reliability data, where maximum likelihood estimates are calculated at successive times during an experiment, but the experiment is only stopped when adequate precision in the censored estimate is obtained. That is, when the censored estimate can provide a reliable guide to the complete estimate. Finally we summarise our results and conclusions, and some ideas for future research are discussed.