This paper presents equations, which can be used to evaluate the failure frequency and the failure rate of a two identical component parallel redundant system in which each component can operate in its wear out period, and the failure rate of each component is exponential power distribution. The optimum maintenance interval for a two identical component parallel redundant system can be obtained using these equations. The proposed approach is presented and illustrated using several numerical examples. The optimum maintenance interval for each component in a two identical parallel redundant system will depend on factors such as: failure rate, repair and maintenance times of each component in the parallel redundant systems.