一般检测维修模型分析

Analyses of General Condition-monitor Maintenance Model

假设设备的寿命服从于一般分布，其检测周期为Ｔ．若设备一旦检测出故障立即进行修理，修理以后，它已不再是开始使用时的状态，而是相当于已使用了一段时间．设Ｙ为这段时间，它是一个随机变量．我们在与第一次维修条件相同的情况下，获得每次设备修理之后Ｙ的分布函数，接着用条件数学期望原理，求得了两个相邻维修区间之间的平均检测次数和平均维修费用．最后以最小总费用作为目标函数，用拉格朗日乘数法，导得了一个最优的检测周期Ｔ．

In this paper we consider that an equipment life is subjected to a general distribution and its condition-monitor cycle time is T. No sooner the failure is monitored than the equipment is repaired. After being repaired, the equipment is notas good as a new one, but is equivalent to one which has been used for a period oftime, let Y indicate such a period of time, then Y is a random variable relating totime for which the equipment has already been operated' Hence, under the samerepair conditions as the first one, we get that Y distribution function after eachbeing repaired. Using the method of condition mean, we can obtain mean condition-monitor times and mean repair cost between two adjacent maintenance intervals. Finally, considering an objective function with bound condition and usingthe Lagrenge multiples method, we obtain a optimum condition-monitor cycletime T, where the minimum total repairing cost is achieved.