Abstract

This study explores an advanced three-parameter generalized log-logistic (GLL) model by incorporating an innovative shape parameter into the conventional log-logistic framework, allowing for greater flexibility in modeling data with increasing, decreasing, and bathtub-shaped failure rates. The estimation challenge under adaptive progressively TypeII censored data is addressed through both classical (likelihood-based) and Bayesian inferential methods. Utilizing observed Fisher information, asymptotic confidence intervals for unknown parameters are derived, while a Markov chain in the Monte Carlo approach is employed to obtain Bayesian point estimates and the highest posterior density intervals. In Bayes’ setup, the GLL parameters are presumed to have independent gamma conjugate priors against various symmetric and asymmetric losses. To examine the accuracy of the acquired estimators, an extensive Monte Carlo simulation is used. Four real-life data sets from the physical and biomedical industries are analyzed to illustrate the feasibility of the proposed techniques in an actual-world scenario. Numerical analyses revealed that the suggested model outperforms the other five models in the literature, including the alpha-power exponential, exponentiated exponential, log-logistic, Weibull, and gamma distributions. The findings emphasize the effectiveness of the Bayesian Markov chain Monte Carlo approach over frequentist techniques, reinforcing its practical significance in reliability analysis and survival studies.OPEN ACCESS Received: 27/03/2025 Accepted: 08/05/2025 Published: 15/08/2025

Abstract

Shasta Reservoir is the largest in California, formed by Shasta Dam on the Sacramento River, and plays a major role in the Central Valley Project (CVP) by providing water storage, flood control, hydroelectric power, and irrigation. This study employs advanced statistical methods to evaluate the reservoir’s reliability and operational risks using censored hydrological data. We propose an improved adaptive progressive censoring plan and apply established statistical techniques, maximum likelihood and maximum product of spacings, alongside Bayesian estimation. The Bayes estimates are obtained through the squared error loss function and based on two sources for the observed data, namely the likelihood and spacing functions. The focus is on estimating the distribution’s scale parameter and two critical reliability metrics: the reliability function and the hazard rate function. The approximate confidence intervals based on the two classical approaches of the scale parameter and reliability metrics are studied. The highest posterior density credible intervals are also discussed. A simulation study evaluates the model’s accuracy under diverse data scenarios, and its practical utility is demonstrated through real-world data from Shasta Reservoir. The problem of optimizing data collection strategies is discussed with the same real data. The findings underscore the model’s value in enhancing reservoir reliability assessments, offering actionable insights for hydrology, disaster preparedness, and sustainable resource management.OPEN ACCESS Received: 15/03/2025 Accepted: 12/06/2025 Published: 22/09/2025

Abstract

This study explores a general framework for reliability analysis named progressive interval Type-I censoring within a multi-stage step-stress partially accelerated life testing setting. A more flexible alternative to the traditional exponential model, known as the length-biased exponential (LBE) distribution, is employed to model failure times. Due to its symmetrical feature, it has extensive applications in real-world domains such as survival analysis, actuarial science, reliability, and mathematical finance. The maximum likelihood approach of estimation is utilized to estimate the model parameters, along with bootstrapping techniques to assess estimation efficiency. Confidence intervals for the LBE parameters are also derived based on asymptotic variances. To optimize the inspection period, two competing optimality criteria—variance minimization (Varoptimality) and determinant maximization (D-optimality)—are investigated. A comprehensive Monte Carlo simulation study is conducted to evaluate the performance of different estimation strategies, demonstrating the superiority of the proposed methodology. Steel is particularly valued for its toughness, wear resistance, and hardness, all of which can be significantly modified through heat treatment and annealing processes. So, a real-world application using hardened steel failure data validates the practical relevance of the developed inferential framework. The findings offer valuable insights for statisticians and reliability engineers in designing efficient life-testing experiments under constrained resources.OPEN ACCESS Received: 21/03/2025 Accepted: 07/05/2025 Published: 22/09/2025

Abstract

Recently, a new bounded version of the Weibull lifetime has been introduced, retaining the flexibility of the standard Weibull model while restricting it to the unit interval, making it particularly useful for betalike modeling in various fields. This paper investigates the improved adaptive Type-II progressively censored plan by applying it to the bounded unit Weibull distribution. From a frequentist perspective, both maximum likelihood and maximum product of spacings methods are used, along with appropriate approximate confidence intervals. Bayesian point estimates, along with Bayesian credible intervals, are obtained using classical procedures that involve Markov-Chain Monte Carlo sampling, with two separate posterior distributions based on the squared error loss. The proposed estimation frameworks encompass both distribution parameters and key reliability metrics, notably the reliability and failure rate functions. Extensive simulations are conducted to evaluate the accuracy and efficiency of the estimators under various censoring levels, sample sizes, and thresholds. To determine the optimal removal strategy under both frequentist estimation paradigms, several metrics are proposed. Additionally, the model is applied to two real-world datasets from engineering reliability; one contains core samples from petroleum reservoirs collected across four cross-sections, and the other pertains to the tensile strength of polyester fibers, illustrating its practical utility and flexibility in modeling. The novelty of this study lies in integrating the bounded support of the unit-Weibull model with an improved adaptive censoring scheme, providing enhanced robustness and adaptability in reliability analysis across different fields.OPEN ACCESS Received: 21/06/2025 Accepted: 19/08/2025 Published: 27/10/2025

Abstract

Shasta Reservoir is the largest in California, formed by Shasta Dam on the Sacramento River, and plays a major role in the Central Valley Project (CVP) by providing water storage, flood control, hydroelectric power, and irrigation. This study employs advanced statistical methods to evaluate the reservoir’s reliability and operational risks using censored hydrological data. We propose an improved adaptive progressive censoring plan and apply established statistical techniques, maximum likelihood and maximum product of spacings, alongside Bayesian estimation. The Bayes estimates are obtained through the squared error loss function and based on two sources for the observed data, namely the likelihood and spacing functions. The focus is on estimating the distribution’s scale parameter and two critical reliability metrics: the reliability function and the hazard rate function. The approximate confidence intervals based on the two classical approaches of the scale parameter and reliability metrics are studied. The highest posterior density credible intervals are also discussed. A simulation study evaluates the model’s accuracy under diverse data scenarios, and its practical utility is demonstrated through real-world data from Shasta Reservoir. The problem of optimizing data collection strategies is discussed with the same real data. The findings underscore the model’s value in enhancing reservoir reliability assessments, offering actionable insights for hydrology, disaster preparedness, and sustainable resource management.OPEN ACCESS Received: 15/03/2025 Accepted: 12/06/2025 Published: 22/09/2025