Full Text Article. Also available at: https://www.worldscientific.com/doi/abs/10.1142/S0218539319500050This paper considers the estimation of stress–strength reliability when two independent exponential inverse Rayleigh distributions with different shape parameters and common scale parameter. The maximum likelihood estimator (MLE) of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error (MSE), bias, average length and coverage probabilities. Finally, a demonstration is delivered on how the proposed reliability model may be applied in data analysis of the strength data for single carbon fibers test data.