Advanced parametric inference and prediction for censored data using standard omega distribution: applications to tensile strength and failure time analysis

Purpose This study presents a framework for parametric inference and prediction of censored data modeled by the standard omega (SO) distribution under progressively Type-II censored sampling schemes. It focuses on developing accurate estimation methods, predicting future failure times, and constructing prediction intervals using classical and Bayesian approaches. Real-world engineering datasets are analyzed to demonstrate the practical applicability of the proposed methodologies to address challenges in engineering involving censored data. Design/methodology/approach Unknown parameters are estimated using MLE, expectation-maximization, product spacing, least squares, and weighted least squares methods, with rigorous demonstration of the existence and uniqueness of MLEs. Confidence intervals are derived using the Fisher information matrix. Bayesian estimation with gamma priors and MCMC methods is applied to compute credible intervals. Prediction methods include best unbiased, conditional median, and Bayesian approaches, with prediction intervals constructed using pivotal, conditional, and HPD techniques. Simulations and optimality criteria guide the selection of sampling schemes, and the methodology is illustrated with two real engineering datasets. Findings The proposed framework proves effective in addressing engineering problems involving censored data. Simulations validate the efficiency of the estimation and prediction methods. Applications to real datasets, such as the tensile strength of polyester fibers and the failure times of Kevlar 49/epoxy strands, showcase the capability of the methods to handle practical scenarios. The comprehensive approach integrates a range of techniques, offering reliable tools for parametric inference in real-world problems. Originality/value The originality of this work lies in its comprehensive approach to parametric inference and prediction for the standard omega distribution under progressively Type-II censored sampling schemes. It integrates diverse estimation methods, including MLE, EM, least squares and Bayesian approaches with gamma priors, while rigorously proving the existence and uniqueness of MLEs. Novel prediction techniques, such as best unbiased and Bayesian methods, are applied alongside innovative prediction interval constructions using pivotal, conditional, and HPD approaches. The study also employs optimality criteria for sampling scheme selection and demonstrates practical applicability through real engineering datasets, establishing a versatile framework for censored data analysis.