Analysis of Weibull time metrics using normal operating via partially accelerated tests with improved adaptive progressive censoring and its applications

Ensuring reliability under normal operating conditions remains a critical challenge in modern industrial systems, where life testing is constrained by time, cost, and safety considerations. This paper proposes a Weibull reliability model analyzed via partially accelerated life tests under normal operating environments, integrated with an improved adaptive progressive censoring scheme to maximize information while minimizing testing duration. The developed methodology bridges the gap between traditional accelerated life testing and realistic operating conditions, enabling precise inference on reliability indices without excessive extrapolation. We derive closed-form expressions for the likelihood function, parameter estimators, and Fisher information, establishing robust inferential procedures for both complete and censored samples. Symmetrical Bayesian frameworks are used for parameter estimation, providing approximate confidence intervals and Bayesian credible intervals to measure uncertainty. A thorough simulation study investigates the finite-sample efficiency of the estimators under various censoring levels and stress profiles. Furthermore, two real datasets, light-emitting diode (LED) lifetime data and insulating liquid breakdown times, are analyzed, illustrating the model's ability to capture complex failure mechanisms and outperform competing Weibull-based schemes in terms of goodness-of-fit and predictive reliability. The proposed framework not only enhances the flexibility of Weibull reliability analysis but also offers practical guidelines for reliability engineers aiming to balance cost, test duration, and information efficiency.