In this paper, we consider the problem of estimating stress-strength reliability for inverse Weibull lifetime models having the same shape parameters but different scale parameters. We obtain the maximum likelihood estimator and its asymptotic distribution. Since the classical estimator doesn't hold explicit forms, we propose an approximate maximum likelihood estimator. The asymptotic confidence interval and two bootstrap intervals are obtained. Using the Gibbs sampling technique, Bayesian estimator and the corresponding credible interval are obtained. The Metropolis-Hastings algorithm is used to generate random variates. Monte Carlo simulations are conducted to compare the proposed methods. Analysis of a real dataset is performed.

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