This paper discusses a new approach for system reliability parameter. Actually, we provide expectation Bayesian (E-Bayesian) estimation of system reliability for Series and parallel systems based on Pascal distribution. The definition and properties of E-Bayesian estimation are given. Also we applied three different distributions for the parameters in prior distribution to investigate the influence of the different prior distributions on the E-Bayesian estimation. The confidence intervals of R, based on E-Bayesian and bootstrap methods, are developed. The performance of these confidence intervals is studied through extensive simulation. Two numerical practical examples, is presented to illustrate the implementation of the proposed procedure.