Advancing reliability analysis for inverted Nadarajah–Haghighi distribution under adaptive progressive censoring with binomial removals

Refah Alotaibi; Mazen Nassar; Ahmed Elshahhat; Refah Alotaibi; Mazen Nassar; Ahmed Elshahhat

doi:10.3934/math.2026979

AIMS Mathematics

2026, Volume 11, Issue 8: 24241-24281. doi: 10.3934/math.2026979

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Advancing reliability analysis for inverted Nadarajah–Haghighi distribution under adaptive progressive censoring with binomial removals

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3.
Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt
4.
Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Received: 28 May 2026 Revised: 08 July 2026 Accepted: 29 July 2026 Published: 10 August 2026
MSC : 62F10, 62F15, 62N01, 62N05

This work introduced a flexible and practically motivated inferential framework for modeling lifetime data under complex and asymmetric settings. In particular, we considered the inverted Nadarajah–Haghighi distribution, a flexible skewed model capable of capturing diverse lifetime behaviors, within an adaptive progressive Type-Ⅱ censoring scheme with random binomial removals. This formulation reflects realistic experimental conditions where the number of removed units varies randomly across stages, providing a more accurate representation of practical reliability and survival studies. Within this framework, statistical inference was developed for the model parameters, the binomial removal parameter, and key reliability measures using both classical and Bayesian approaches. Maximum likelihood estimation was obtained via numerical optimization, and approximate confidence intervals were constructed based on the observed Fisher information matrix. From a Bayesian perspective, independent gamma priors were assumed for the model parameters, while a beta prior was specified for the binomial removal parameter. Posterior inference was carried out using Markov chain Monte Carlo methods to obtain point estimates and corresponding credible intervals. A comprehensive simulation study was conducted to assess the performance of the proposed estimators under various configurations of sample size and model parameters. Finally, the applicability and effectiveness of the proposed methodology were demonstrated through the analysis of two real datasets arising from environmental toxicology and economic geology.
- inverted Nadarajah–Haghighi distribution,
- reliability measures,
- adaptive progressive censoring,
- binomial removal,
- loss function
Citation: Refah Alotaibi, Mazen Nassar, Ahmed Elshahhat. Advancing reliability analysis for inverted Nadarajah–Haghighi distribution under adaptive progressive censoring with binomial removals[J]. AIMS Mathematics, 2026, 11(8): 24241-24281. doi: 10.3934/math.2026979

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Abstract

This work introduced a flexible and practically motivated inferential framework for modeling lifetime data under complex and asymmetric settings. In particular, we considered the inverted Nadarajah–Haghighi distribution, a flexible skewed model capable of capturing diverse lifetime behaviors, within an adaptive progressive Type-Ⅱ censoring scheme with random binomial removals. This formulation reflects realistic experimental conditions where the number of removed units varies randomly across stages, providing a more accurate representation of practical reliability and survival studies. Within this framework, statistical inference was developed for the model parameters, the binomial removal parameter, and key reliability measures using both classical and Bayesian approaches. Maximum likelihood estimation was obtained via numerical optimization, and approximate confidence intervals were constructed based on the observed Fisher information matrix. From a Bayesian perspective, independent gamma priors were assumed for the model parameters, while a beta prior was specified for the binomial removal parameter. Posterior inference was carried out using Markov chain Monte Carlo methods to obtain point estimates and corresponding credible intervals. A comprehensive simulation study was conducted to assess the performance of the proposed estimators under various configurations of sample size and model parameters. Finally, the applicability and effectiveness of the proposed methodology were demonstrated through the analysis of two real datasets arising from environmental toxicology and economic geology.

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