Statistical inference for the Weibull distribution under improved adaptive Type-Ⅱ progressive censoring with binomial removals

An improved adaptive type-Ⅱ progressive censoring (IAT-Ⅱ PC) scheme has been introduced to effectively control the duration of life-testing experiments within a prespecified limit. While this scheme has attracted considerable attention, statistical inference under random removals, in which the number of removals at each failure time is treated as a random variable, remains largely unexplored in the literature. In this paper, we focus on statistical inference for the two-parameter Weibull distribution based on the IAT-Ⅱ PC scheme, where the number of removals at each failure time follows a binomial distribution. Point and interval estimation of the Weibull parameters was carried out using the maximum likelihood (ML), maximum product spacing (MPS), and Bayesian estimation methods. Asymptotic confidence intervals for the model parameters were constructed based on the asymptotic normality of the ML and MPS estimators. Since the posterior distributions are analytically intractable, Bayesian estimates and their corresponding credible intervals were obtained using the Markov Chain Monte Carlo method. The performance of the proposed estimators was evaluated through an extensive Monte Carlo simulation study. In addition, a real-world dataset was analyzed to demonstrate the practical applicability of the proposed inference methods. The results show that the Bayesian estimators yield more accurate point and interval estimates than their classical counterparts under the IAT-Ⅱ PC scheme with binomial removals.