A New Multi-Progressive Generalized Type-II Censoring: Theory, Reliability Inference, and Multidisciplinary Applications

Modern reliability experiments frequently face operational constraints that require balancing test duration, precision, and removal strategies, rendering classical censoring schemes inadequate for contemporary multidisciplinary applications. This study introduces a novel multi-progressive generalized Type-II censoring (MP-GC-T2) framework that unifies and extends existing progressive and generalized censoring structures through the integration of staged failure-proportion controls, dual temporal termination thresholds, and adaptive withdrawal of surviving units. The proposed mechanism provides enhanced flexibility in experiment design while retaining analytical tractability for statistical inference. Assuming Weibull lifetimes, we develop a complete inferential framework including maximum likelihood estimation, asymptotic interval construction, and Bayesian estimation via hybrid Metropolis–Hastings–Gibbs sampling with informative gamma priors, together with multiple interval estimation strategies for reliability characteristics. Extensive Monte Carlo investigations assess estimator bias, precision, coverage behaviour, and interval efficiency across diverse censoring configurations, demonstrating robustness and inferential gains relative to conventional schemes. Furthermore, optimal progressive-removal planning criteria are explored to guide practitioners in selecting censoring patterns that maximize inferential accuracy under practical constraints. The versatility and practical relevance of the MP-GC-T2 design are illustrated through applications to heterogeneous real datasets arising from clinical, chemical, geological, physical, and petroleum sciences, confirming its adaptability to distinct reliability structures and data-generation mechanisms. Collectively, the proposed methodology contributes a unified experimental and inferential platform that advances censoring design, reliability estimation, and cross-disciplinary statistical modelling.