Stress–Strength Reliability Inference with Upper Record Ranked Set Sampling Under the Scale-Parameter Exponential Family

In reliability engineering and life-testing experiments, exact measurements can be costly or destructive, whereas ranking information and upper record observations are often easier to obtain. Upper record ranked set sampling (RRSS) provides an efficient design for such settings, and the scale-parameter exponential family (SPEF) offers a unified framework covering several common lifetime distributions. Motivated by these advantages, this paper investigates point and interval estimation of the stress–strength reliability parameter R under upper RRSS and SPEF assumptions. Explicit expressions for the maximum likelihood estimator and the uniformly minimum variance unbiased estimator of R are derived, and their performance is evaluated. To address inference limitations in small samples, Bayesian point and highest posterior density (HPD) interval estimators are developed via Monte Carlo simulation under conjugate gamma priors. Several frequentist confidence intervals are also constructed, including an exact interval, an approximate MLE-based interval, and three parametric bootstrap intervals. Simulation studies demonstrate that the Bayesian HPD intervals attain nominal coverage with competitive expected lengths in small samples. Finally, the practical utility and model adequacy of the proposed methodologies are demonstrated through an analysis of real lifetime data from steel specimens.