For this thesis a model to determine the minimum reliability requirement for, multiple components within a system that will yield the goal reliability value for the system, the model consists of two parts . The first part is a nonlinear programming formulation of the allocation problem . The second part is a cost function formulation to be used in the nonlinear programming algorithm. Direct search methods ( Modified Hooke-Jeeve's and Complex method) are used to solve the allocation problem. Also reliability important of components (Ii) used in this model. The model have yielded very encouraging results and it can be applied to any type of system , simple or complex, and for a variety of distributions . The advantages of this model are very flexible. All programs are coded in Pascal on pentium 4. These advantages make the proposed reliability allocation solution a great system design tool.