This paper is concerned with a repair vs replacement problem for a system observed in continuous time and subject to random failure. When the system fails, a decision is taken, based on the observed values of the (random) repair cost and system's age, to either perform a minimal repair or to replace the system by a new one. At any time, the system may also be replaced preventively, and the aim of the decision maker is to minimize the total expected discounted cost. A dynamic programming approach is proposed to solve this problem. Sufficient conditions under which a repair-limit rule is optimal are given, an efficient algorithm is devised for the computation of such an optimal policy, and a numerical illustration is worked out.