TTT transforms and age replacements with discounted costs

The ordinary age replacement problem consists of finding an optimal age at which a unit, needed in a continuous production process, should be replaced in order to minimize the average long‐run cost per unit time. Bergman introduced a graphical procedure based on the total‐time‐on‐test (TTT) concept for the analysis of the age replacement problem. In this article, that idea is generalized to the situation of discounted costs. We also study a more general age replacement problem in which we have a form of imperfect repair.