2026-10-11T20:22:05Z https://api.figshare.com/v2/oai

oai:figshare.com:article/33752660 2026-09-14T18:54:15Z category_21 category_734 category_811 category_69 category_106 portal_87 item_type_3 month_year_09_2026

Higher-order likelihood-based inference for Weibull models Chunling Luo (758664) Shixiang Li (8402067) Piao Chen (765144) Biotechnology Biological Sciences not elsewhere classified Mathematical Sciences not elsewhere classified Inorganic Chemistry Science Policy accelerated life testing confidence interval interval estimation reliability small sample <p>Weibull models are a central tool for reliability assessment, where engineers often need accurate confidence intervals for shape, scale and low lifetime quantiles under small samples, censoring and accelerated life testing. 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. Simulation studies across a wide range of shapes, sample sizes and designs show that the proposed intervals achieve coverage very close to the nominal level. A case study on breakdown times of an insulating fluid under accelerated testing illustrates the practical gains in estimating low use-stress quantiles.</p> 2026-09-14T18:54:15Z Dataset Dataset 10.6084/m9.figshare.33752660.v1 https://figshare.com/articles/dataset/Higher-order_likelihood-based_inference_for_Weibull_models/33752660 CC BY 4.0