This paper's intent is to present a new approach for enhancing system reliability by utilizing the ability of certain systems to tolerate interruptions in their basic function for a specific period of time without violation the mission success definition. One can use this time for auxiliary functions, to redo a specified task or to repair failed equipment. In this paper, this capability is called time-redundancy. A reliability model is developed for a system with time-redundancy. Using this reliability model, the Laplace transform of the time distribution function between failures is derived. A particular case of the exponential initial distribution is studied to show the advantages of utilizing time-redundancy. A practical example is provided.