Without considering that the component which alternates between operating and storage states periodically is likely new after each repair, the method of equivalent failure time of time-sharing redundant system is studied, and the cumulative damage model is put forward. Basing on Weibull distribution, the model is developed and its parameters are estimated, and a simulation method for evaluating system reliability is also given. Finally, an example about 1-out-of-3 mechanical system is given to demonstrate the affectiveness of the model.