This paper is concerned with the analysis of the reliability of complex systems in which components are used intermittently and which are maintained in operating condition by component replacement. The idea that a failed component causes system failure only when it is called into use is expressed mathematically. Based on component failure distributions and usage properties, the system reliability and expected time to system failure are derived as functions of system age for two different maintenance policies. With both policies, a component is replaced whenever it causes system failure. In the first, this is the only maintenance, while in the second, system check-outs are conducted at fixed intervals and all components which have failed without causing system failure are replaced. The two policies are compared and, for the second, the dependence of system reliability on the maintenance interval is determined.