基于工作周期的最优出保随机维修策略

兰州理工大学学报 ›› 2023, Vol. 49 ›› Issue (3): 153-164.

基于工作周期的最优出保随机维修策略

尚利俊¹, 杜永军^*2,*, 张苾雯²

1.佛山科学技术学院质量与标准化学院, 广东佛山 528225;
2.兰州理工大学经济管理学院, 甘肃兰州 730050

收稿日期:2022-04-06 出版日期:2023-06-28 发布日期:2023-07-07
通讯作者: 杜永军(1977-),男,陕西渭南人,博士,副教授. Email:yjdu@lut.edu.cn
基金资助:
国家自然科学基金(72161025,12072139,71871181),广东省基础与应用基础研究基金(2020A1515011360),广东省教育厅项目(2021WTSCX080)

Optimum post-warranty random maintenance policy based on working cycles

SHANG Li-jun¹, DU Yong-jun², ZHANG Bi-wen²

1. School of Quality Management and Standardization, Foshan University, Foshan 528225, China;
2. School of Economics and Management, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2022-04-06 Online:2023-06-28 Published:2023-07-07

摘要/Abstract

摘要： 将有限数量工作周期和补偿方案同时融入到更新比例收费更换保修(RPRW)中,提出了一个保证产品可靠性性能的二维保修,即“考虑补偿的二维更新比例收费更换保修(2DRPRW with R)”. 此外,从消费者角度将2DRPRW with R 扩展到出保维修中,提出了一个维持出保可靠性的出保随机维修策略,即“随机周期更换(RPR)策略”. 构建了RPR产生的费用率模型、得出特殊费用率模型. 采用数值实验对2DRPRW with R和RPR开展了灵敏性分析. 数值结果表明,与更新比例收费更换保修相比,通过限制随机工作周期数量,2DRPRW with R的保修费用能够被控制.

关键词: 工作周期, 保修, 出保可靠性, 随机周期更换, 费用率

Abstract: By incorporating both limited number of working cycles and a refund into renewing pro-rata replacement warranty (RPRW), a two-dimensional renewing pro-rata replacement warranty with refund (2DRPRW with R) is proposed, which can help manufacturers to ensure product reliability performance. Besides, by extending 2DRPRW with R to the post-warranty maintenance, a post-warranty random maintenance is modeled from consumers’ perspective to sustain post-warranty reliability, which is called random periodic replacement (RPR) policy. The cost rate model produced by RPR is constructed, and some special cost rates are obtained. Finally, the sensitivities of the proposed approaches are analyzed in numerical experiments. It shows that the warranty cost of 2DRPRW with R can be controlled by limiting the number of working cycles compared to RPRW.

Key words: working cycle, warranty, post-warranty reliability, random periodic replacement, cost rate

中图分类号:

O213

尚利俊, 杜永军, 张苾雯. 基于工作周期的最优出保随机维修策略[J]. 兰州理工大学学报, 2023, 49(3): 153-164.

SHANG Li-jun, DU Yong-jun, ZHANG Bi-wen. Optimum post-warranty random maintenance policy based on working cycles[J]. Journal of Lanzhou University of Technology, 2023, 49(3): 153-164.

参考文献

[1] CHA J H,FINKELSTEIN M,LEVITIN G.Optimal warranty policy with inspection for heterogeneous,stochastically degrading items[J].European Journal of Operational Research,2021,289(3):1142-1152.
[2] ZHANG N,FOULADIRAD M,BARROS A.Evaluation of the warranty cost of a product with type III stochastic dependence between components[J].Applied Mathematical Modelling,2018,59:39-53.
[3] SHANG L,SI S,SUN S,et al.Optimal warranty design and post-warranty maintenance for products subject to stochastic degradation[J].IISE Transactions,2018,50(10):913-927.
[4] WANG L Y,PEI Z N,ZHU H H,et al.Optimising extended warranty policies following the two-dimensional warranty with repair time threshold[J].Eksploatacja i Niezawodnosc-Maintenance and Reliability,2018,20(4):523-530.
[5] 贾云献,李欣玥,王鹏,等.考虑多故障模式的新型装备更新保修费用预测[J].系统工程与电子技术,2015,37(8):1810-1817.
[6] 张怀强,李铁成,杜军岗.舰载导弹系统故障率及保修期模型优化[J].系统工程与电子技术,2022,44(1):347-356.
[7] HE Z,WANG D,HE S,et al.Two-dimensional extended warranty strategy including maintenance level and purchase time:A win-win perspective[J].Computers & Industrial Engineering,2020,141:106294.
[8] YE Z S,MURTHY D N P.Warranty menu design for a two-dimensional warranty[J].Reliability Engineering & System Safety,2016,155:21-29.
[9] XIE W,SHEN L,ZHONG Y.Two-dimensional aggregate warranty demand forecasting under sales uncertainty[J].IISE Transactions,2017,49(5):553-565.
[10] SU C,WANG X.A two-stage preventive maintenance optimization model incorporating two-dimensional extended warranty[J].Reliability Engineering & System Safety,2016,155:169-178.
[11] HOOTI F,AHMADI J,LONGOBARDI M.Optimal extended warranty length with limited number of repairs in the warranty period[J].Reliability Engineering & System Safety,2020,203:107111.
[12] LIU B,WU J,XIE M.Cost analysis for multi-component system with failure interaction under renewing free-replacement warranty[J].European Journal of Operational Research,2015,243:874-882.
[13] WANG X,HE K,HE Z,et al.Cost analysis of a piece-wise renewing free replacement warranty policy[J].Computers & Industrial Engineering,2019,135:1047-1062.
[14] SHANG L,CAI Z.Optimal replacement policy of products with repair-cost threshold after the extended warranty[J].Systems Engineering and Electronics,2017,28(4):725-731.
[15] PARK M,JUNG M,PARK D H.Optimization of periodic preventive maintenance policy following the expiration of two-dimensional warranty[J].Reliability Engineering & System Safety,2018,170:1-9.
[16] LIU P,WANG G,SU P.Optimal maintenance strategies for warranty products with limited repair time and limited repair number[J].Reliability Engineering & System Safety,2021,210:107554.
[17] PARK M,JUNG K M,PARK D H.Warranty cost analysis for second-hand products under a two-stage repair-or-full refund policy[J].Reliability Engineering & System Safety,2020,193:106596.
[18] LIU P,WANG G,SU P.Optimal replacement strategies for warranty products with multiple failure modes after warranty expiry[J].Computers & Industrial Engineering,2021,153:107040.
[19] PARK M,JUNG K M,PARK D H.A generalized age replacement policy for systems under renewing repair-replacement warranty[J].IEEE Transactions on Reliability,2016,65:604-612.
[20] SHANG L,SI S,CAI Z.Optimal maintenance-replacement policy of products with competing failures after expiry of the warranty[J].Computers & Industrial Engineering,2016,98:68-77.
[21] ZHAO X,NAKAGAWA T.Optimization problems of replacement first or last in reliability theory[J].European Journal of Operational Research,2012,223:141-149.
[22] CHANG C C.Optimum preventive maintenance policies for systems subject to random working times,replacement,and minimal repair[J].Computers & Industrial Engineering,2014,67:185-194.
[23] SHEU S H,LIU T H,ZHANG Z G.Extended optimal preventive replacement policies with random working cycle[J].Reliability Engineering & System Safety,2019,188:398-415.
[24] ZHAO X,NAKAGAWA T,ZUO M.Optimal replacement last with continuous and discrete policies[J].IEEE Transactions on Reliability,2014,63:868-880.
[25] 曹晋华,程侃.可靠性数学引论 [M].北京:高等教育出版社,2006.
[26] BOLAND P J,PROSCHAN F.Periodic replacement with increasing minimal repair costs at failure[J].Operations Research,1982,30(6):1183-1189.
[27] CHIEN Y.Optimal periodic replacement policy for a GPP repairable product under the free-repair warranty[J].Quality Technology & Quantitative Management,2018,16(3):347-354.
[28] ULLAH A,JIANG W.Optimal periodic replacement policy for a warranted product subject to multi modes failure process[J].Journal of Management Analytics,2019,6(2):154-172.