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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (12): 2390-2396    DOI: 10.3785/j.issn.1008-973X.2021.12.020
电子、通信与自动控制技术     
考虑协变量的设备退化和生产批量整合模型
刘学娟1(),赵斐2
1. 北京科技大学 经济管理学院，北京 100083
2. 东北大学秦皇岛分校 管理学院，河北 秦皇岛 066004
Integrated model of system degradation and production lot sizing with considering covariate
Xue-juan LIU1(),Fei ZHAO2
1. School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China
2. School of Management, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
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摘要：

运用随机系数回归模型对设备的退化过程进行建模，基于加速失效时间模型在退化过程分析中加入协变量的影响，并在模型中考虑产品质量问题. 运用更新回报定理建立状态监测维修和经济生产批量的整合费用模型.优化分析整合费用模型，可以得到决策变量的最优值. 通过数值案例分析，得到设备运行状态最优的预防性维修阈值、最优经济生产批量. 结果表明，随着协变量的逐渐增加，最优生产批量逐渐减小，最优预防性维修阈值没有变化. 通过敏感性分析进一步说明模型相关参数对最优解的影响.
关键词： 退化过程;  经济生产批量;  加速失效时间模型;  协变量;  更新回报定理    
Abstract:

The system degradation process was modeled by random coefficient regression model, in which the covariate was considered based on the accelerated failure time model, and the product quality was also considered in the model. The integrated cost model of condition-based maintenance and economic production quantity was proposed based on renewal reward theory. The optimal value of decision variables could be obtained by analyzing the integrated cost model. The optimal critical level of preventive maintenance and the optimal lot size were obtained by analysis of numerical case. Result shows that the optimal lot size decreases gradually with the increasing of covariate, but the optimal critical level of preventive maintenance does not change. Influence of optimal results caused by relevant parameter is explained by sensitive analysis.
Key words: degradation process    economic production quantity    accelerated failure time model    covariate    renewal reward theory
收稿日期: 2021-02-26 出版日期: 2021-12-31
CLC:  TB 114.3  
基金资助: 国家自然科学基金资助项目(71601019, 71701038, 71871018)；河北省自然科学基金资助项目(G2019501074)；教育部人文社会科学研究资助项目(16YJC630174)；中央高校基本科研业务费专项资金资助项目（FRF-IPPE-2102）
作者简介: 刘学娟(1982—), 女, 副教授, 博士, 从事系统健康管理研究. orcid.org/0000-0002-8520-1711. E-mail: liuxj@ustb.edu.cn
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引用本文:

刘学娟,赵斐. 考虑协变量的设备退化和生产批量整合模型[J]. 浙江大学学报(工学版), 2021, 55(12): 2390-2396.

Xue-juan LIU,Fei ZHAO. Integrated model of system degradation and production lot sizing with considering covariate. Journal of ZheJiang University (Engineering Science), 2021, 55(12): 2390-2396.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.12.020    或    https://www.zjujournals.com/eng/CN/Y2021/V55/I12/2390

图 1  生产过程和设备退化过程中的PM更新
图 2  设备退化过程与生产过程中的故障更新
图 3  不同协变量取值情况下的单位时间期望费用
X $\tau^*$/d $C^*$/丝 ${E_{\rm{C}}}(\tau^*;C^*)$/(元·d?1)
0.1 1.45 2.55 123.6
0.2 1.42 2.55 125.5
0.3 1.40 2.56 127.5
0.4 1.38 2.56 129.5
0.5 1.36 2.56 131.6
0.6 1.33 2.56 133.7
0.7 1.31 2.56 135.8
0.8 1.29 2.56 138.1
0.9 1.27 2.56 140.3
表 1  不同协变量取值情况下的参数最优解
$ {C_f} $/元 $\tau^*$/d $C^*$/丝 ${E_{\rm{C}}}(\tau^*;C^*)$/(元·d?1)
300 2.61 4.0 105.3
400 1.81 3.34 120.2
500 1.39 2.56 128.1
600 1.28 2.52 131.3
700 1.21 2.51 133.4
800 1.17 2.50 135.0
表 2  X=1/3时不同单位故障维修费用情况下的参数最优解
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