Extended Optimal Replacement Policy for a Two-Unit System With Shock Damage Interaction


In this paper, we tend to contemplate a system consisting of 2 major units, A and B, each subject to two sorts of shocks that occur consistent with a non-homogeneous Poisson method. A sort II shock causes a whole system failure which is corrected by a replacement; and a kind I shock causes a unit A minor failure, that is rectified by a minimal repair. The shock sort likelihood is age-dependent. Every unit A minor failure ends up in a random amount of damage to unit B. Such a injury to unit B will be accumulated to a specified level of the whole system failure. Moreover, unit B with a cumulative harm of level z may become minor failed with chance π(z) at every unit A minor failure, and fixed by a minimal repair. We tend to consider a a lot of general replacement policy where the system is replaced at age T, or the Nth sort I shock, or 1st type II shock, or when the whole injury to unit B exceeds a specified level, whichever occurs 1st. We tend to verify the optimal policy of T* and N* to reduce the s-expected cost per unit time. We gift some numerical examples, and show that our model is that the generalization of many previous maintenance models within the literature.

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