Statistical inference of some coherent systems in stress-strength setup

This dissertation considers stress-strength reliability estimation of a consecutive 𝑘-out of- 𝑛 system for identical and non-identical strength components when the stress and strength variables belong to the proportional hazard rate model. Estimation methods of the system reliability are applied under the classical and Bayesian perspectives. All point and interval estimations are derived in cases of the second parameters of underlying distributions are common and unknown, and different and known. Then, corresponding asymptotic confidence intervals and highest probability density credible intervals are also obtained for all cases. Comparison of the proposed estimates is presented through Monte Carlo simulations for each case. Finally, the implementation of proposed methods is analyzed by real data sets.