In this thesis the redundancy allocation problem has been studied in great detail to select the required design configurations. The reliability of multistage system that consists of several components in series may be improved in two ways: either using more reliable components or redundant components. Since the first approach (reliable components) is not always suitable, the second approach (redundant components) is more commonly adopted. Therefore, the aim of this thesis is to select a component and redundancy level to maximize the reliability of entire system. The optimal reliability design problem for an n-stages in series has m-parallel redundancy components are also represented via an integer nonlinear programming model, viz. as a series-parallel design configuration. Different improvement optimization algorithms have been built, such as, ratio method, integer nonlinear programming and redundancy optimization methods to obtain an optimal solution.