Abstract
Conditional confidence sets for one and two Weibull reliability levels at fixed times with minimum sizes are determined using an equivalent objective Bayesian perspective. The methodology is applicable even when standard Type II or progressive censorship is present. The proposed confidence sets fulfill the Likelihood and Sufficiency Principles, as well as the Conditionality Principle, whereas typical unconditional sets based on maximum likelihood estimators and other insufficient statistics violate those principles. Hypothesis testing is performed on the basis of the smallest-size confidence sets. A simulation-based approach is also developed to derive shortest-length confidence intervals and minimum-area confidence regions, in addition to conduct hypothesis tests. An example involving failure times of an insulating fluid is explored for illustrative purposes.
Published Version
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