In some practical situations, it would be impossible to conduct a replacement action for an operating system during the middle of a job and might be wise to wait until the completion of its operation. First, this paper considers age replacement policies for a system, which continuously works for multiple jobs with random working times. Next, the system can undergo minimal repairs upon failures and is replaced at the first completion of the working time over a planned time T. Finally, when a job incurs some damage to the system, the replacement model over time T is applied. The expected cost rates for these modified models are derived, and the optimal maintenance policies, which minimize the expected cost rates are obtained analytically. Copyright © 2012 John Wiley & Sons, Ltd.