Higher-order likelihood-based inference for Weibull models

Standard likelihood-based intervals rely only on first-order asymptotics and can show substantial undercoverage, while existing refined methods are either tabulated for very specific settings or difficult to extend to more complex designs.

We develop a unified higher-order likelihood framework for interval estimation in Weibull and log-Weibull models that treats any scalar parameter or reliability characteristic, including use-stress quantiles in accelerated tests, as the parameter of interest. Using the modified signed likelihood root together with an analytically constructed canonical parameter, we obtain simple closed-form adjustment factors that require no external tables and are valid for complete data, Type II censoring and accelerated life testing with log-linear scale models.