多维随机向量传递机制下的RV-GERT网络模型及其解析算法  

RV-GERT Network and Its Analytical Algorithm with Multi-dimensional Random Vector Transfer Mechanism

作　　者：董文杰[1] 刘思峰[1] 方志耕[1] 曹颖赛 张习习 DONG Wen-jie;LIU Si-feng;FANG Zhi-geng;CAO Ying-sai;ZHANG Xi-xi(College of Economics and Management, Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学经济与管理学院,江苏南京210016

出　　处：《系统工程》2018年第2期55-62,共8页Systems Engineering

基　　金：国家自然科学基金资助项目(71671091);欧盟第7研究框架玛丽居里国际人才引进计划Fellow项目(FP7-PIIF-GA-2013-629051);中央高校基本科研业务费专项科研项目(NP2015037;NP2015208);南京航空航天大学校研究生创新基地(实验室)开放基金立项项目(kfjj20170906);中国博士后科学基金资助项目(2018M630561)

摘　　要：通过构建多维随机向量传递关系下的RV-GERT网络基本模型,利用n维空间内的多元Copula函数将网络传递活动上随机变量的联合分布函数和各自的边缘分布函数连接起来,进而推导节点活动间等价传递参量的度量形式。定义了随机向量矩母函数的概念,借助于信号流图理论分析网络等价拓扑关系,应用梅森公式和矩母函数的性质设计RV-GERT网络的解析算法。通过对RV-GERT网络中传递变量、矩母函数和W函数三者的等价转化,可以求解网络中任意活动的实现概率、期望、方差和风险度等基本参数,从而一定程度上可拓展GERT理论的应用范围。案例对某商用飞机有限公司研制的一款新型数据记录装置的研发周期、产品重量和电池供电时间等技术指标进行分析,利用RV-GERT网络解析算法进行参数反演,并与传统多个参量单独传递的解析算法进行对比,证明所建模型的科学性和实用性。By constructing the RV-GERT network model transferred with n-dimensional random variable, joint distribution function of the random variables on directed branches and marginal distribution function of each variable are connected by using the multivariate Copula function in n-dimensional space, the joint probability density function of the random variables then can be deduced. The concept of moment generating function （m. g. f. ） of multi-dimensional random is proposed. With signal flow-graphs theory, the equivalent topological relations are analyzed, and by using Mason formula and characteristics of m. g. f. , analytical algorithm of RV-GERT network is designed. By implementing equivalent conversions of transmit variable, m. g. f. and W-function, the basic parameters in RV-GERT network such as probability, expectation, variance and relative risk can be solved, so as to extend the application range of GERT theory. The case studies the development cycle, product weight and battery power time of a new data recording device developed by a commercial aircraft Co. , Ltd. , and uses the analytic algorithm of RV-GERT network to inverse the parameters, which shows the science and practicability of the model.

关 键 词：GERT网络 多维随机变量 COPULA函数 解析式算法 报信者系统 

分 类 号：F224[经济管理—国民经济]