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A geometric process repair model for a series repairable system with k dissimilar components

机译：具有k个不同组件的可修复系列系统的几何过程修复模型

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摘要

In this paper, a geometric process repair model for a k-dissimilar-component series repairable system with one repairman is proposed. For each component, the successive operating times form a decreasing geometric process whereas the consecutive repair times constitute an increasing geometric process. Under this assumption, we consider a replacement policy M = (N_1, N_2,..., N_k) based respectively on the number of failures of component 1, component 2, ..., and component k. Our problem is to determine an optimal replacement policy M~* = (N_1~*,N_2~*,...,N_k~*) such that the average cost rate (i.e. the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived and the corresponding optimal replacement policy can be determined analytically or numerically. Finally, an appropriate numerical example is given to illustrate some issues included the sensitivity analysis and the uniqueness of the optimal replacement policy M~*.
机译：本文提出了一个具有一个修理工的k-异种分量系列可修理系统的几何过程修理模型。对于每个组件，连续的工作时间形成递减的几何过程，而连续的维修时间构成增加的几何过程。在此假设下，我们分别根据组件1，组件2，...和组件k的故障数量，考虑替换策略M =（N_1，N_2，...，N_k）。我们的问题是确定最佳替换策略M〜* =（N_1〜*，N_2〜*，...，N_k〜*），以使平均成本率（即单位时间的长期平均成本）最小化。得出平均成本率的显式表达式，并可以通过分析或数字确定相应的最佳替换策略。最后，给出一个适当的数值例子来说明一些问题，包括敏感性分析和最优替换策略M〜*的唯一性。

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