双贮备系统冷/温/热贮备模型的优化选择研究

Research on Optimal Selection for Cold/Warm/Hot-standby Patterns of Dual-standby Systems

对运行设备安装双贮备设备是实现系统高可靠性的有效方法.在双贮备系统冷/温/热三种贮备模型中,选择哪种贮备模型对系统性能指标和经济指标均有重要影响,因此对如何选择双贮备系统的贮备模型从而使系统性能最优或经济效益最大的问题进行研究具有现实意义.而现有研究成果很少涉及双贮备系统贮备模型的优化选择问题.为此,本文创新性地提出一种确定双贮备系统最优贮备模型的选择方法.分别建立系统冷/温/热贮备模型,分析每个模型的系统状态及系统半Markov核函数,利用Markov更新方程、Laplace变换以及Laplace-Stieltjes变换技术推导系统稳态可用度、稳态平均维修次数、维修人员稳态忙期概率以及冷贮备模型的平均激活时间,并从经济角度给出系统单位时间内的净收益函数.最后分别以性能指标和经济指标作为研究目标,通过模型对比分析给出不同条件下的系统贮备模型的优化选择算法,并对每个研究目标下的优化选择算法进行实例计算.计算结果表明以不同性能指标和不同费用作为参考得出的最优贮备模型不尽相同,从而验证了所提方法能够有效地确定不同衡量标准下的系统最优贮备模型.

It is an effective way to realize the system high reliability by installing dual-standby device.Among the three standby models of cold,warm and hot,which standby model to select has a significant impact on the system performance and economic indicators.However,existing research works rarely involved the optimal selection of standby models.Thus,this study innovatively presents an approach to determine the optimal standby mode for dual-standby systems.The models of cold,warm and hot standby are constructed respectively,and system states and corresponding state transition probabilities of each model are analyzed.Subsequently,the availability,average number of maintenance,probability of the repairman busying and average activation time of the cold standby system in steady state are deduced using the Markov renewal equation,Laplace transform and Laplace-Stieltjes transform technologies.Furthermore,the function with respect to net revenue per unit time of the system is given from the viewpoint of economic principles.Finally,the optimal selection algorithm of the system standby model under different conditions is given in terms of performance and economic indicators through comparative analysis among models,and numerical examples of optimal selection algorithm in each objective are given based on a practical application.The numerical results demonstrate that the obtained optimal standby pattern is not always the same when taking different performance indicators and different costs as references,which validates that the presented approach can effectively determine the optimal system standby model under different indicators.