The stress-strength analysis is widely applied to engineering and many other scientific fields. In this article, we focus on the estimation of the stress-strength parameter for a decreasing failure rate model, i.e., the exponential-Poisson distribution, when the collection of informative data is based on three different sampling schemes, namely the simple random sampling scheme, ranked set sampling scheme, and the maximum ranked set sampling procedure with unequal sample sizes. Both classical and Bayesian methods are employed to find the point and interval estimators for the stress-strength parameter. The Metropolis-Hastings within Gibbs algorithm is proposed to approximate the Bayes point estimates. We present a simulation study, as well as an example, for the purpose of illustration and comparison. The results show that the ranked set sampling scheme outperforms the other two schemes.
