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The deterioration of a system is often caused by an internal cause, such as aging and accumulated system wear. Another reason for system deterioration could be an external cause such as an environmental factor. For example, if a computer is attacked by some virus, then the operating time of the computer is reduced or the computer can fail. Thus, when studying a maintenance problem for a repairable system, one should not only consider the internal cause but consider the effect of a random shocks produced by the environment against the system.
In most of the research works for the simple repairable system, a common assumption is to assume that the system will be repaired as soon as it fails. In fact, it is not always the case. In practice, for example, the system after failure cannot be repaired immediately because the repairman is on vacation. This will cause a delayed repair time. 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.
Most of the maintenance models just pay attention on the internal cause of the system failure, but not on an external cause. A system failure may be caused by some external causes, such as a shock. In a δ-shock model, the system fails if the time interval between two successive shocks falls below a fixed threshold δ.
In an extended extreme shock maintenance model, shock is called a deadly shock if the amount of damage of one shock to the system exceeds a specific threshold so that the system will fail. In practice, a deteriorating system after repair should be more weak and easier to be broken down. As a result, the threshold value, which a deadly shock exceeds, will be decreasing in n , the number of repairs taken.
In chapter 2, we have introduced a partial product process. Fundamental results relating to Partial Product Process have been established. We have proved that it is a monotone Process. Mean and variance of Partial Product Process have been determined. We studied its application to maintenance model for a deteriorating system under policy N. The long run average cost under policy N is derived. Existence of optimality under the Policy N is derived. Numerical example is given to illustrate the results developed in this chapter.
In chapter 3, the maintenance model for a deteriorating system under which successive operating times follows geometric process and successive repair times follows partial product process is studied. An explicit expression for the long run average cost per unit time under N policy is derived and an optimal policy N* for minimizing the long run average cost per unit time is determined analytically. Numerical example is given to illustrate the results developed in this chapter.
In chapter 4, the maintenance model for a deteriorating system under a random environment using partial product process is studied. An explicit expression for the long-run average cost per unit time under the replacement policy N is developed. An optimal policy N* for minimizing the long run average cost per unit time is determined analytically. A numerical example is given to explain the methodology used.
In chapter 5, the maintenance model for a deteriorating system with imperfect delayed repair under partial product process is studied. The long run average cost under policy N is derived. Existence of optimality under the Policy N is derived. Numerical example is given to illustrate the results developed in this chapter.
In chapter 6, the maintenance model for a deteriorating system with imperfect delayed repair using partial product process under bivariate replacement policy (T, N) is studied. An explicit expression for the long-run average cost per unit time under the bivariate replacement policy (T, N) is determined.
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