The optimal replacement for additive damage models in discrete setting
A system receives shocks at successive random points of discrete time, and each shock causes a positive integer-valued random amount of damage which accumulates on the system one after another. The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold. Upon failure the system must be replaced by a new and identical one and a cost is incurred. If the system is replaced before failure, a lower cost is incurred. On the basis of some assumptions, we specify a replacement rule which minimizes the long-run (expected) average cost per unit time and possesses the control limit property, Finally, an algorithm is discussed in a special case.
Key wordsIncreasing homogeneous Markov chain first failure time optimal average replacement cost optimal replacement policy λ-minimization technique compound binomial sequence
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