Stress–strength reliability estimation under the standard two-sided power distribution

•The stress–strength model based on the two-sided power distribution is considered.•An expression for the stress-strength reliability is obtained exactly.•Methods for estimating of the stress–strength reliability are given.•Comparison of estimation methods are made through simulation studies.•A real data application to see the performances of the estimators is given. In this report, the distribution for setting up a system reliability exposed to some stress is studied. The standard two-sided power distribution is assumed to be the underlying distribution. We obtained the exact expressions and estimates for the reliability by applying different methods such as maximum likelihood and Bayesian estimators. Three different scenarios were examined: known and equal reflection parameters, known but unequal reflection parameters, and all parameters are unknown, providing practical guidance and recommendations for the estimator design. For large samples, we recommend use of the parametric bootstrap method with the maximum likelihood estimate. Real data sets were used to illustrate the performances of the estimators.