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) warm (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.