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The paper considers the prediction of reliability for a complex system designed for continuous operation. The state of the system is defined by identifying the subsystems which are functioning, the remainder undergoing repair (no inactive standby). The system is described as up whenever it is in one of an arbitrarily selected set of the system states. It is assumed that maintenance facilities are always adequate, and that the system conforms to a few other very mild restrictions. An exponential failure law is not assumed. Formulas are developed giving the mean durations of system up-times and down-times in terms of the corresponding quantities for the subsystems. The sensitivities of the formulas to errors in the input data are considered.