Bayesian and Classical Survival Inference for the Nadarajah–Haghighi Model under Unified Type-I Progressive Hybrid Censoring with Random Binomial Removals

Abstract

A highly adaptable censoring framework, known as the unified TypeI progressive hybrid censoring scheme, has been recently introduced as an enhancement to the unified hybrid censoring approach. However, this censoring method has a significant limitation: it assumes that the removal pattern is fixed and established prior to conducting the experiment, which may lack practical applicability. This study presents, for the first time, the unified Type-I progressive hybrid censoring scheme incorporating binomial removal, which enables the random withdrawal of surviving units following each failure, making it more suitable for survival studies. Assuming that the underlying distribution of the test units follows the Nadarajah–Haghighi distribution, we examine both point and interval estimation problems for the model parameters, binomial parameter, and two key survival measures. Maximum likelihood estimation serves as the classical methodology for obtaining point estimates and approximate confidence intervals. For Bayesian estimation, we employ the squared error loss function in conjunction with Markov Chain Monte Carlo sampling techniques. A comprehensive simulation analysis is conducted to assess the performance of the various point and interval estimators. In addition, to demonstrate the practical relevance of the proposed methodologies in survival analysis, a real-world data application involving the death times of a group of 45 gastric cancer patients is investigated.OPEN ACCESS Received: 02/11/2025 Accepted: 11/12/2025 Published: 21/07/2026

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