An economic discrete replacement policy for a shock damage model with minimal repairs |
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Authors: | Min-Tsai Lai Bor-Yuh Leu |
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Affiliation: | Department of Industrial Engineering and Management, Nan-Tai College, Tainan, Taiwan, R.O.C.;Department of Industrial Engineering and Management, Minghsin Institute of Technology and Commerce, Hsinchu, Taiwan, R.O.C. |
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Abstract: | A discrete replacement model for a repairable system which is subject to shocks and minimal repairs is discussed. Such shocks can be classified, depending on its effect to the system, into two types: Type I and Type II shocks. Whenever a type II shock occurs causes the system to go into failure, such a failure is called type II failure and can be corrected by a minimal repair. A type I shock does damage to the system in the sense that it increases the failure rate by a certain amount and the failure rate also increases with age due to aging process without external shocks; furthermore, the failure occurred in this condition is called type I failure. The system is replaced at the time of the first type I failure or the n-th type Il failure, whichever occurs first. Introducing costs due to replacement and mininal repairs, the long-run expected cost per unit time is derived as a criterion of optimality and the optimal number n∗ found by minimizing that cost. It is shown that, under certain conditions, there exists a finite and unique optimal number n∗. |
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