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This paper aims to investigate the optimization of the replacement with minimal repair policy for a system which experiences a time horizon of random length. Under such policy system replacement occurs at multiples of some period while minimal repair is performed at system failure between two successive replacements.

The objective function is the expected total cost composed of minimal repairs and replacements costs. A simple and compact expression is derived for the expected total costs and conditions under which an optimal replacement period exits are given. For sake of illustration, a numerical example is provided.

The paper finds that by the recent great technological development, the life cycle of present products is seen to be reduced more and more. This has motivated the development of maintenance optimization models for systems which experience an exact finite time horizon.

To ensure the benefits from the improved technologies, the information concerning the technological change must be taken into account. Such information is based on technological forecasting and difficult to obtain and merely rely on uncertainties.