In lifetime and reliability analyses, the Rayleigh distribution is extensively employed to model components or systems characterized by an increasing failure rate. On the other hand, in recent years, the improved adaptive Type-II progressive censoring scheme (IAT-II PCS) has gained considerable attention for its ability to ensure that the testing process concludes within a predetermined time. However, in many real-world applications, the number of units removed at each failure time cannot be predetermined precisely, which renders randomly determined removals a more realistic modeling assumption. Motivated by these considerations, this study focuses on estimating the scale parameter and reliability characteristics of the Rayleigh distribution under the IAT-II PCS with random removals. For this purpose, the maximum likelihood (ML) estimators are used alongside the Bayesian estimators derived under the squared error loss function. An extensive Monte Carlo simulation study is carried out to assess the performance of these estimators. Furthermore, a real data application is included to demonstrate the practical relevance of the proposed approaches. The results indicate that Bayesian estimators based on informative prior achieve better performance in terms of mean square error under the IAT-II PCS with binomial random removals
GEZER et al. (Fri,) studied this question.