Three different time-dependent optimal reliability design models with a series-parallel system are formulated. An efficient heuristic procedure for each problem is elucidated, and the results are described. The redundancy optimization problem using the time-dependent reliability function is solved so that the system reliability exceeds the target reliability over a time period at a minimum cost. The number of the redundancies in the system is obtained to ensure that the target reliability can be matched with the system reliability, which is time-dependent, as closely as possible without violating a cost constraints. The system configuration is optimized so that the system reliability matches the target reliability as much as possible while maintaining the system reliability at certain level under a cost constraint. Various applications of simple and efficient heuristic algorithms for solving time-dependent redundancy optimization problems are also provided. These techniques are used and tested in systems containing a substantial number of subsystems. The heuristic approaches appear more successful than other optimization techniques in solving these problems, and can be applied to any constrained redundancy optimization problems without any tedious formulation and computation. / Master of Science