The load optimization of a repairable system with gamma-distributed time-to-failure

Reliability Engineering Pub Date : 1987-01-01 DOI:10.1016/0143-8174(87)90032-1

Jerzy Filus

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引用次数: 8

Abstract

We consider a system which supports a load in such a way that the profit earned by the system for one time unit is a continuous and increasing function of the amount of the load. The time-to-failure distribution of the system is assumed to be gamma. Both parameters of the distribution are continuous functions of the load such that the mean time-to-failure is a decreasing function of the load.

The system earns the profit only when it is on. When it is off, it is repaired, and the losses are assumed to be proportional to the repair time. We define the average asymptotic gain earned by the system in a single time unit; this quantity can be thought of as a system efficiency measure.

Assuming that the load is a controllable variable, the goal is to find a value of the load that maximizes the so-defined efficiency. To model the relationship between the load and the parameters of the time-to-failure distribution (gamma) as well as the relation between the load and the profit, power and exponential functions have been taken.

The analytical conditions for the existence of maximum positive gain and the analysis of the behaviour of the gain as the load varies are presented.

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具有分布故障时间的可修系统的负荷优化

我们考虑这样一个系统，它以这样的方式支持负荷，即系统在一个时间单位内获得的利润是负荷量的连续递增函数。假设系统的失效时间分布为。分布的两个参数都是荷载的连续函数，因此平均失效时间是荷载的递减函数。系统只有在运行时才会盈利。当它关闭时，它被修复，并且假定损耗与修复时间成正比。我们定义了系统在单个时间单位内获得的平均渐近增益;这个数量可以被认为是一个系统效率度量。假设负载是一个可控变量，目标是找到一个使所定义的效率最大化的负载值。为了模拟负荷与失效时间分布(gamma)参数之间的关系以及负荷与利润之间的关系，采用了幂函数和指数函数。给出了最大正增益存在的解析条件，并分析了增益随负载变化的特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Reliability Engineering

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