Resumen
Confidence regions for the Weibull parameters with minimum areas among all those based on the Conditionality Principle are constructed using an equivalent diffuse Bayesian approach. The process is valid for scenarios involving standard failure and progressive censorship, and complete data. Optimal conditional confidence sets for two Weibull quantiles are also derived. Simulation-based algorithms are provided for computing the smallest-area regions with fixed confidence levels. Importantly, the proposed confidence sets satisfy the Sufficiency, Likelihood and Conditionality Principles in contrast to the unconditional regions based on maximum likelihood estimators and other insufficient statistics. The suggested perspective can be applied to parametric estimation and hypothesis testing, as well as to the determination of minimum-size confidence sets for other invariantly estimable functions of the Weibull parameters. A dataset concerning failure times of an insulating fluid is studied for illustrative and comparative purposes.