A δ- shock maintenance model for a deteriorating system with imperfect delayed repair under partial product process

There are some systems in real life that cannot be repaired immediately, if they fail, but repairs are not always delayed. In different words, once the system fails, the repair is sometimes delayed and the repair is sometimes immediate. This kind of repair is referred to as the imperfect delayed repair(IDR). In a δ-shock model, a shock is a deadly shock, if the time interval between two successive shocks is smaller than the specified threshold δ. In this paper, a δ-shock maintenance model for a deteriorating system with imperfect delayed repair under partial process is studied. A replacement policy N is adopted by which the system is replaced by an identical new one at the time following the N-th failure. The long-run average cost per unit time is then evaluated and the corresponding optimal policy is determined analytically. A numerical example is given.