One of the most challenging concepts in reliability analysis is estimating the stress-strength parameter, \(\beta = P(Z < T).\) The estimate of \(\beta\) is frequently criticized for being unstable and weak in the face of high values and outliers. The contribution examines the problem of estimating \(\beta\) in the presence of outliers when stress (Z) and strength (T) random variables have exponentiated half-logistic-based models with the same scale parameter and dissimilar shape parameters. The reliability estimates of \(\beta\) are investigated using classical and Bayesian methods, based on homogeneous situations and outliers, under the assumption that stress (Z) and strength (T) are independent. The maximum likelihood reliability estimator of \(\beta\) is calculated for the conventional technique. Additionally, a Bayesian estimator for \(\beta\) is given with independent gamma priors. One may derive Bayesian estimators using symmetric and asymmetric loss functions. The implementation of Markov chain Monte Carlo techniques has been employed for some sophisticated calculations. The accuracy of various \(\beta\) estimates is examined using simulation. The provided methodology is ultimately applied to two real-world datasets from the insurance and physical studies. An investigation showed that better estimates for both strategies were obtained with higher sample numbers. Overall, both approaches' accuracy metrics declined as the number of outliers increased. Under the precautionary loss function, the Bayesian estimates consistently performed better than the observed estimates under the other loss functions.
