One of the most critical challenges in progressively Type-II censored data is determining the removal plan. It can be fixed or random so that is chosen according to a discrete probability distribution. Firstly, this paper introduces two discrete joint distributions for random removals, where the lifetimes follow the two-parameter Weibull distribution. The proposed scenarios are based on the normalized spacings of exponential progressively Type-II censored order statistics. The expected total test time has been obtained under the proposed approaches. The parameters estimation are derived using different estimation procedures as the maximum likelihood, maximum product spacing and least-squares methods. Next, the proposed random removal schemes are compared to the discrete uniform, the binomial, and fixed removal schemes via a Monte Carlo simulation study in terms of their biases; root means squared errors of estimators and their expected experiment times. The expected experiment time ratio is also discussed under progressive Type-II censoring to the complete sampling plan. 

Unlike traditional methods that assume removals are independent of the failure process, this paper presents a novel approach for classical and Bayesian inference under progressive Type-II censoring with informative random removals. Under a Weibull-Poisson lifetime model, two removal distributions—the truncated Poisson and truncated discrete Weibull—are introduced. Due to their structural dependence on the model parameters, these distributions enhance estimation accuracy under heavy censoring. Finally, the superiority of the proposed methods is evaluated through Monte Carlo simulations and the analysis of real data on remission times of bladder cancer patients.