Abstarct: In this thesis, the probability of failure-free operation until time t, along with the probability of stress-strength, baxsed on different sampling designs consist of ranked set sampling, record ranked set sampling and progressive censoring data is studied in a family of lifetime distributions, specially exponential distribution. For estimation and improving purposes, the preliminary test and Stein-type shrinkage estimators are proposed and their exact distributional properties are derived. For numerical superiority demonstration of the proposed estimation strategies, some improved bootstrap confidence Intervals, are constructed. An extensive simulation study is carried out in order to assess the performance of the methods. Simulation evidences revealed that our proposed shrinkage strategies perform well in the estimation of parameters baxsed on mentioned sampling designs. These strategies applied on some real data and evaluated their results. ‎