Replacement Policies under Minimal Repair
Replacement Policies under Minimal Repair
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DOI：
10.1057/jors.1981.114
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发表时间：
1981-07
影响因子：
3.6
通讯作者：
R. I. Phelps
中科院分区：
文献类型：
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作者：
R. I. Phelps
在许多情况下，系统发生故障时，“最小修复”的概念是很重要的。最低限度的修复发生在故障系统没有被处理，以使其返回到“新的”条件，而是返回到平均条件的工作系统的年龄。例如，复杂的系统，其中一个部件的维修或更换不会对整个系统的状况产生实质性影响。对于可靠性下降的系统，通过最小限度的维修来维持运行将变得越来越昂贵，于是出现了何时更换整个系统的问题。我们考虑的情况下，故障分布可以模拟威布尔分布。针对这一情况提出了两项政策。一种是定时更换，另一种是固定故障次数更换。我们考虑了第三种策略，即在固定时间后的下一次故障时更换，并证明了它是最优的，导出了决定更换点和该策略的费用的表达式。不幸的是，这些不会引起显式表示，因此它们被用来提供广泛的数值比较的政策，在搜索有效的显式近似。从这些比较得出结论的政策和近似的相对有效性。
In many situations where system failures occur the concept of ‘minimal repair’ is important. A minimal repair occurs when the failed system is not treated so as to return it to ‘as new’ condition but is instead returned to the average condition for a working system of its age. Examples include complex systems where the repair or replacement of one component does not materially affect the condition of the whole system.For a system with decreasing reliability it will become increasingly expensive to maintain operation by minimal repairs, and the question then arises as to when the entire system should be replaced. We consider cases where the failure distribution can be modelled by the Weibull distribution. Two policies have been suggested for this case. One is to replace at a fixed time and the other is to replace at a fixed number of failures. We consider a third policy, to replace at the next failure after a fixed time, and show that it is optimal.Expressions to decide the replacement point and the cost of this policy are derived. Unfortunately these do not give rise to explicit representations, and so they are used to provide extensive numerical comparisons of the policies in a search for effective explicit approximations. Conclusions are drawn from these comparisons regarding the relative effectiveness of the policies and approximations.