Estimation for multicomponent reliability is considered when underlying strength and stress variables follow unit inverse exponentiated distributions. We discuss structural properties for this distribution and then illustrate its applications in reliability engineering. Different estimators of reliability are derived from frequentist and Bayesian viewpoints. Maximum likelihood and Bayes estimators are discussed when a common parameter is unknown. Confidence intervals are constructed as well. Further uniformly minimum variance unbiased and exact Bayes estimators are obtained for the case common parameter is known. Point and interval estimators are compared numerically using simulations. Analysis of a real data set is presented for illustration purposes.