Analysis of Burr-XII Lifespan Using Adaptive Progressive Type-II Hybrid Binomial Censoring with Physical Modeling of Polyester and Carbon Fibers

Abstract

This study introduces advanced statistical methods, allowing for more efficient and accurate reliability testing of fibers such as polyester and carbon. Polyester ficbers are suitable for textiles and industrial use due to their wrinkle resistance and affordability, while carbon fibers offer superior strength, thermal stability, and corrosion resistance. To guarantee greater efficiency of inference methodologies and reduce overall testing time, the adaptive Type-II progressive hybrid censoring via binomial removals has gained popularity in reliability analysis and life-testing problems. The proposed scheme allows survival units to be removed at random stages according to a binomial law, thereby reducing experimental time while preserving statistical efficiency. When lifetimes are gathered using the suggested censoring technique, point and interval estimates of the unknown parameters of the Burr-XII model are obtained using both classical and Bayesian approaches. We obtain various Bayesian estimates using the squared loss function. Some numerical methods are employed to obtain the suggested estimators due to their complexity. The various Bayes estimates and related credible intervals are created using Markov chain Monte Carlo techniques. To assess estimator performance, extensive simulation studies are conducted, comparing bias, mean squared error, coverage probabilities, and interval lengths under varying censoring and removal settings. The simulation results confirm that the Bayesian framework, particularly with informative priors, provides more accurate and stable estimates than asymptotic likelihood-based methods. We examine two physics data sets representing polyester and carbon fibers to demonstrate the relevance of the suggested approaches in a real-world setting. These applications highlight the practical value of the proposed approach for material design, maintenance planning, and broader reliability engineering problems.OPEN ACCESS Received: 13/06/2025 Accepted: 12/09/2025 Published: 23/01/2026

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