Adapting an age-reduction model to extend the useful-life duration

Most of the proposed age-reduction models was introduced and widely used in applications only for the case of monotonically increasing failure rates. However, from a practical perspective, there are several situations for which failure rates are decreasing or bathtub shaped. In these cases, the existing imperfect maintenance models may lead to the restoration of a system to the infant mortality period and can be considered as harmful. In this paper, we modify the usual assumptions on traditional age-reduction models to take into account the bathtub-shaped failure rates. Finally, we provide a numerical example to illustrate our result.