Optimum Analysis and Parameter Inference of a New Improved Adaptive Progressive Unit-Weibull Model Censoring with Two Physical Applications

Abstract

Recently, a new bounded version of the Weibull lifetime has been introduced, retaining the flexibility of the standard Weibull model while restricting it to the unit interval, making it particularly useful for betalike modeling in various fields. This paper investigates the improved adaptive Type-II progressively censored plan by applying it to the bounded unit Weibull distribution. From a frequentist perspective, both maximum likelihood and maximum product of spacings methods are used, along with appropriate approximate confidence intervals. Bayesian point estimates, along with Bayesian credible intervals, are obtained using classical procedures that involve Markov-Chain Monte Carlo sampling, with two separate posterior distributions based on the squared error loss. The proposed estimation frameworks encompass both distribution parameters and key reliability metrics, notably the reliability and failure rate functions. Extensive simulations are conducted to evaluate the accuracy and efficiency of the estimators under various censoring levels, sample sizes, and thresholds. To determine the optimal removal strategy under both frequentist estimation paradigms, several metrics are proposed. Additionally, the model is applied to two real-world datasets from engineering reliability; one contains core samples from petroleum reservoirs collected across four cross-sections, and the other pertains to the tensile strength of polyester fibers, illustrating its practical utility and flexibility in modeling. The novelty of this study lies in integrating the bounded support of the unit-Weibull model with an improved adaptive censoring scheme, providing enhanced robustness and adaptability in reliability analysis across different fields.OPEN ACCESS Received: 21/06/2025 Accepted: 19/08/2025 Published: 27/10/2025

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