可修排队系统备件灰色生灭预测模型  

Grey BD prediction model for spare parts of repairable queuing system

作　　者：陈顶[1,2] 方志耕 刘思峰[1] CHEN Ding;FANG Zhigeng;LIU Sifeng(College of Economics and Management,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;Department of Management Science,University of Waterloo,N2J 2Z2,Canada)

机构地区：[1]南京航空航天大学经济与管理学院,南京211106 [2]滑铁卢大学管理科学系,加拿大N2J 2Z2

出　　处：《系统工程理论与实践》2020年第5期1326-1338,共13页Systems Engineering-Theory & Practice

基　　金：玛丽居里欧盟第7框架人才引进计划(FP7-PIIF-GA2013-629051);国家自然科学基金(91324003);国家社科基金重点研究项目(12AZD102);江苏省自然科学基金(14GLC008)。

摘　　要：可修部件的失效率和修复率在服役周期内呈现不确定性,基于确定型失效率和修复率建模的生灭过程在解决可修部件备件预测问题时存在一定局限.传统可修备件需求预测模型忽视了排队维修情况下的讨论,这与工程实际不符.以服从一般分布的区间灰数表征可修部件的失效率与修复率,构建了灰色状态转移矩阵,建立了一类排队维修系统的可修部件备件灰色生灭预测模型,研究了该过程的无记忆性和稳态解的存在条件,讨论了失效修复比、修理能力、备件数量与保障率的性质.一定程度上揭示了修理能力受限、失效修复比不确定背景下的可修系统备件需求规律.实际案例验证了模型的有效性和实用性.During the life cycle,the failure rate and repairable rate of repairable parts shows uncertain characteristics.The birth and death process based on the determined failure rate and repair rate may not meet the demand forecasting of spare parts.The traditional repairable spare parts demand forecast model ignores the case of queuing maintenance,which is inconsistent with engineering practice.By using gray numbers to represent the failure rate and repair rate of repairable parts,the gray state transition matrix is constructed.A spare parts demand forecasting model of repairable queuing system based on gray birth and death process was raised.The memoryless and existence conditions of steady solution of the process based on gray birth and death are studied.The characteristics of failure-repair ratio,repair worker numbers,spare parts quantity and guarantee rates were discussed.To some extent,the spare parts demand law with the uncertain information of the failure rate and the repair rate is revealed.The practical case study verifies the validity and practicability of the model.

关 键 词：灰色系统理论 生灭过程 可修排队 备件需求 蒙特卡罗仿真 

分 类 号：N941.5[自然科学总论—系统科学]