Delay-time concept has been used in a large number of applications for modelling important aspects of reality, such as the dynamics of failures, which in practice occurs in two stages for the most devices. Concisely, a defect arises in a component or system followed by a subsequent failure after an interval called delay time. The effort to repair a defect is related to the time from when it can be firstly observed until its discovery by an inspection. However, a small number of contributions deal with the cost related to the time in which the system undergoes in the defective state. In addition, a repair action on a system that undergoes in defective state for a short period of time can have different consequences than the same action after a long period of time. Two examples are: a pipeline leakage defect and the repair of a defect in a tooth. In both cases, the consequences vary depending on the time in defective state. Hence, this paper proposes a way to take the defect cost into consideration according to the time in which the system undergoes in this state.