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

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.