We consider the problem of determining the optimal replacement policy of the items which deteriorate appreciably with time and become obsolete. Most of the conventional engineering economy models including the widely-accepted MAPI model assume linearity of technological improvement over time, in obtaining the economic lives of items and the net present values of the replacement alternatives under consideration. The main achievement of this paper is in that it successfully relaxes this strict linearity assumption to accommodate various other types of technological improvements in determining those values. Based on these results, we also include in this paper the mathematical models by which to determine the optimal replacement policies of items both under and without capital budgeting constraints.