This paper presents a periodic replacement policy under minimal repair when a system undergoes random durations of operations. The system is put in operation and then idle for some time. The time durations of each use(operation) are random variables. During the idle times, system experiences no aging. Under the proposed policy, system is re-placed at the end of the use duration after some cumulative use time elapses. The failures during use durations are minimally repaired instantaneously. The cost rate expressions under the policy is derived for exponential use durations. It is shown that under some conditions there exists a finite optimum value of the control variable. Numerical examples are presented to demonstrate the result.