Summary: We consider a \(k\)-out-of-\(n\) system with repair under \(T\)-policy. Life time of each component is exponentially distributed with parameter \(\lambda\). Server is called to the system after the elapse of \(T\) time units since his departure after completion of repair of all failed units in the previous cycle or until accumulation of \(n-k\) failed units, whichever occurs first. Service time is assumed to be exponential with rate \(\mu\). \(T\) is also exponentially distributed with parameter \(\alpha\). System state probabilities in finite time and long run are derived for (i) cold (ii) worm (iii) hot systems. Several characteristics of these systems are obtained. A control problem is also investigated and numerical illustrations are provided. It is proved that the expected profit to the system is concave in \(\alpha\) and hence global maximum exists.