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Bayesian estimation and credible interval of stress–strength reliability R = P(X < Y) for two-parameter bathtub-shaped lifetime (TPBL) distribution are considered based on simple random sampling (SRS), ranked set sampling (RSS) and maximum ranked set sampling with unequal samples (MRSSU). Monte Carlo simulations are used to compare the performances of different proposed methods for Bayesian inferences on R. The results of simulation show that the estimator of the stress–strength reliability based on MRSSU and RSS are more efficient than SRS. Also, we make a comparison between the performance of the proposed methods in this paper and Tarvirdizade and Ahmadpour’s [Estimation of the stress–strength reliability for the two-parameter bathtub-shaped lifetime distribution based on upper record values. Stat Methodol. 2016;31:58–72] method, which is based on upper record values. Finally, a real data set has been analyzed for illustrative purposes.