This paper deals with the study of stress-strength model represented by \(R=P[Y<X<Z]\) , wherein system failure occurs when the inherent strength X of the system is either lower or higher than the threshold limits of stress (Y or Z). The stress-strength parameter R is studied under progressive type-II censored samples, where the strength variable X, and the stress variables Y and Z, are assumed to follow independent Weibull half-logistic distribution characterized by the same shape parameter but distinct scale parameter. In the classical setup, we proposed the maximum likelihood estimator, approximate maximum likelihood estimator, and asymptotic confidence intervals for R. In the Bayesian paradigm, the Bayes estimate of R and the corresponding credible interval for R are obtained under the squared error loss function, using independent gamma priors for the unknown parameters. The study involves Monte-Carlo simulation to illustrate the efficacy of the proposed methods. Additionally, to verify the effectiveness of our suggested model, a dataset on the strength of single carbon fibers is examined.
