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On Optimal Replacement Policy for a Generalized Model  

Ji Hwan Cha (Division of Mathematical Sciences, Pukyong National University)
Publication Information
Journal of Korean Society for Quality Management / v.31, no.3, 2003 , pp. 185-192 More about this Journal
Abstract
In this paper, the properties on the optimal replacement policies for the general failure model are developed. In the general failure model, two types of system failures may occur : one is Type I failure (minor failure) which can be removed by a minimal repair and the other, Type II failure (catastrophic failure) which can be removed only by complete repair. It is assumed that, when the unit fails, Type I failure occurs with probability 1-p and Type II failure occurs with probability p, $0\leqp\leq1$. Under the model, the system is minimally repaired for each Type I failure, and it is repaired completely at the time of the Type II failure or at its age T, whichever occurs first. We further assume that the repair times are non-negligible. It is assumed that the minimal repair times in a renewal cycle consist of a strictly increasing geometric process. Under this model, we study the properties on the optimal replacement policy minimizing the long-run average cost per unit time.
Keywords
Optimal Maintenance Policy; General Failure Model; Long-run Average Cost Rate; Geometric Process;
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