Computational analysis of generalized progressive hybrid log-logistic model and its modeling for physics and engineering applications

Heba S. Mohammed; Osama E. Abo-Kasem; Ahmed Elshahhat; Heba S. Mohammed; Osama E. Abo-Kasem; Ahmed Elshahhat

doi:10.3934/math.2025487

AIMS Mathematics

2025, Volume 10, Issue 5: 10709-10739. doi: 10.3934/math.2025487

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Computational analysis of generalized progressive hybrid log-logistic model and its modeling for physics and engineering applications

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 Commerce, Zagazig University, Zagazig 44519, Egypt
3.
Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Received: 06 March 2025 Revised: 16 April 2025 Accepted: 24 April 2025 Published: 09 May 2025
MSC : 62F10, 62F15, 62N01, 62N02, 62N05

Modern products often have long life cycles and high reliability, making it difficult to collect comprehensive product life data with all unit failures for reliability and quality analysis. So, a new sampling plan called the generalized Type-Ⅱ progressive hybrid censored strategy has been suggested to minimize test time and costs. This study introduces a novel statistical framework for modeling lifetime data under generalized progressive hybrid censoring using the log-logistic (LogL) lifespan model. Besides traditional methodologies, our approach integrates frequentist and Bayesian inferential techniques to estimate key parameters and reliability metrics, such as the survival and hazard functions of the LogL distribution. The relevant approximate confidence intervals for unknown numbers are also constructed using the frequentest estimators' normal approximations. Incorporating the Markovian technique into Bayesian analysis, we leverage independent gamma priors and the Metropolis-Hastings algorithm to enhance computational efficiency to calculate the Bayes' point estimators along with their highest posterior density interval estimators. Additionally, we propose an optimal progressive censoring scheme that minimizes experimental costs while maintaining estimation accuracy. Extensive Monte Carlo simulations confirm the superiority of the proposed estimators, while three real-world applications in physics and engineering demonstrate their practical efficacy. The findings highlight the versatility of the LogL model and its potential as a robust survival analysis tool under complex real-world conditions.
- log-logistic,
- Markovian iterative chain,
- inference,
- optimum plan,
- physics and engineering data modeling
Citation: Heba S. Mohammed, Osama E. Abo-Kasem, Ahmed Elshahhat. Computational analysis of generalized progressive hybrid log-logistic model and its modeling for physics and engineering applications[J]. AIMS Mathematics, 2025, 10(5): 10709-10739. doi: 10.3934/math.2025487

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Abstract

Modern products often have long life cycles and high reliability, making it difficult to collect comprehensive product life data with all unit failures for reliability and quality analysis. So, a new sampling plan called the generalized Type-Ⅱ progressive hybrid censored strategy has been suggested to minimize test time and costs. This study introduces a novel statistical framework for modeling lifetime data under generalized progressive hybrid censoring using the log-logistic (LogL) lifespan model. Besides traditional methodologies, our approach integrates frequentist and Bayesian inferential techniques to estimate key parameters and reliability metrics, such as the survival and hazard functions of the LogL distribution. The relevant approximate confidence intervals for unknown numbers are also constructed using the frequentest estimators' normal approximations. Incorporating the Markovian technique into Bayesian analysis, we leverage independent gamma priors and the Metropolis-Hastings algorithm to enhance computational efficiency to calculate the Bayes' point estimators along with their highest posterior density interval estimators. Additionally, we propose an optimal progressive censoring scheme that minimizes experimental costs while maintaining estimation accuracy. Extensive Monte Carlo simulations confirm the superiority of the proposed estimators, while three real-world applications in physics and engineering demonstrate their practical efficacy. The findings highlight the versatility of the LogL model and its potential as a robust survival analysis tool under complex real-world conditions.

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