The problem of estimating the reliability characteristics of parallel systems with spares and/or repairable elements is investigated. A parallel system is such that the failure of all units causes failure of the entire system. Under very general assumptions, we have found, among others, an upper as well as a lower bound on the mean time before failure of a parallel system withnindependent units. An example is given in detail to illustrate how the theorems proved in section 2 can be applied and the main theorem is stated in section 4. Some bounds on the higher moments of the time to failure are treated in [l].