Statistical inference for a one-parameter lifetime model under unified progressive hybrid censoring with binomial random removals

Ehab M. Almetwally; Ehab M. Almetwally

doi:10.3934/math.2026009

AIMS Mathematics

2026, Volume 11, Issue 1: 211-242. doi: 10.3934/math.2026009

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Statistical inference for a one-parameter lifetime model under unified progressive hybrid censoring with binomial random removals

Ehab M. Almetwally ^{1,2
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1.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
2.
Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11152, Egypt

Received: 02 October 2025 Revised: 04 December 2025 Accepted: 22 December 2025 Published: 04 January 2026
MSC : 62N02, 62F15, 62N05

A unified progressive hybrid censoring scheme is introduced by combining progressive and hybrid plans, allowing tests to be terminated either after a predetermined number of failures or at a fixed time. Both likelihood and Bayesian procedures are developed for estimating the parameter, reliability, and hazard rate of a one-parameter lifetime model when data are generated under this scheme. Maximum likelihood estimates are obtained via the Newton-Raphson algorithm, and asymptotic confidence intervals are constructed using the delta method with the Fisher information matrix. In addition, parametric bootstrap methods are employed for constructing confidence intervals. Within the Bayesian framework, Markov chain Monte Carlo techniques are employed under non-informative and informative independent gamma priors, with computational intractability addressed through the Metropolis-Hastings algorithm. Progressive censoring with binomial random removals has also been considered within this framework to enhance flexibility in test termination and data collection. Extensive Monte Carlo simulations are conducted to compare the efficiency of the likelihood and Bayesian estimators across multiple censoring designs, and the superiority of Bayesian inference with informative priors is demonstrated. The applicability of the proposed estimators is illustrated using three real datasets: tensile strength of polyester fibers, aircraft air-conditioning failures, and ordered failure times. The one-parameter model is further compared with ten standard unit distributions. The censoring framework is successfully applied to these datasets, confirming its practical value in modeling reliability and failure behavior.
- progressive hybrid censoring,
- binomial random removals,
- one-parameter lifetime model,
- maximum likelihood,
- Bayesian inference,
- MCMC,
- reliability
Citation: Ehab M. Almetwally. Statistical inference for a one-parameter lifetime model under unified progressive hybrid censoring with binomial random removals[J]. AIMS Mathematics, 2026, 11(1): 211-242. doi: 10.3934/math.2026009

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Abstract

A unified progressive hybrid censoring scheme is introduced by combining progressive and hybrid plans, allowing tests to be terminated either after a predetermined number of failures or at a fixed time. Both likelihood and Bayesian procedures are developed for estimating the parameter, reliability, and hazard rate of a one-parameter lifetime model when data are generated under this scheme. Maximum likelihood estimates are obtained via the Newton-Raphson algorithm, and asymptotic confidence intervals are constructed using the delta method with the Fisher information matrix. In addition, parametric bootstrap methods are employed for constructing confidence intervals. Within the Bayesian framework, Markov chain Monte Carlo techniques are employed under non-informative and informative independent gamma priors, with computational intractability addressed through the Metropolis-Hastings algorithm. Progressive censoring with binomial random removals has also been considered within this framework to enhance flexibility in test termination and data collection. Extensive Monte Carlo simulations are conducted to compare the efficiency of the likelihood and Bayesian estimators across multiple censoring designs, and the superiority of Bayesian inference with informative priors is demonstrated. The applicability of the proposed estimators is illustrated using three real datasets: tensile strength of polyester fibers, aircraft air-conditioning failures, and ordered failure times. The one-parameter model is further compared with ten standard unit distributions. The censoring framework is successfully applied to these datasets, confirming its practical value in modeling reliability and failure behavior.

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