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. (C) 2018 Elsevier Inc. All rights reserved.