基于Markov过程的冗余系统备件与冗余度联合优化
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摘要
为了合理有效地降低冗余系统全寿命周期费用,同时考虑部件的故障过程、维修周转以及备件的订购补给过程,结合混合准则提出了基于Markov过程的k/n冗余系统可用度模型,实现备件库存配置与冗余度联合优化。首先,通过热备份和冷备份模式下的系统故障率和修复率计算公式,建立了使用可用度模型。然后,基于稳态概率计算全寿命周期费用,并运用备件库存配置与冗余度联合优化算法实现模型的求解。最后,通过数值计算验证可用度模型的正确性以及联合优化的有效性。通过数值计算结果表明,所提出的可用度模型是传统模型的有益改进并且具有普适性。联合优化算例结果显示,冗余系统可用度随冗余度或备件库存的增加而得到提升,而当可用度接近1时若要进一步提高可用度将导致费用急剧增长;全寿命周期费用中备件存储费用的所占比例最高,而备件订购费用最低;算例表明,与仅考虑备件库存优化的方法相比,联合优化使全寿命周期费用降低了8.01%。
To reasonably and efficiently decrease the life cycle cost of a redundant system,this paper proposes an availability model of a k/nbased on the Markov process and mixed criterion to perform joint optimization of spare parts inventory allocation and the redundancy level,by considering the failure process,maintenance turnover and the ordering and replenishment process of spare parts.The availability model is firstly established through the formula of system failure rate and maintenance rate in hot standby and cold standby modes.Then the life cycle cost is calculated based on the steady-state probability,and the joint optimization algorithm of spare parts inventory allocation and the redundancy level is used to solve the model.Finally,the correctness of the availability model is validated and the validity of the joint optimization is verified by numerical calculation.Through the numerical calculation results,it is shown that the proposed availability model is an improvement of the traditional model and processes the universality.The joint optimization results show that the redundancy system availability increases with the increase of the redundancy level and the spare parts inventory.However,further improvement of availability will lead to a sharp increase in cost when it is close to 1.The proportion of spare parts inventory cost is the highest in the life cycle cost,while the spare parts ordering cost is the lowest.Compared with the method that only considers spare parts inventory optimization,the life cycle cost of the joint optimization method is reduced by 8.01%.
To reasonably and efficiently decrease the life cycle cost of a redundant system,this paper proposes an availability model of a k/nbased on the Markov process and mixed criterion to perform joint optimization of spare parts inventory allocation and the redundancy level,by considering the failure process,maintenance turnover and the ordering and replenishment process of spare parts.The availability model is firstly established through the formula of system failure rate and maintenance rate in hot standby and cold standby modes.Then the life cycle cost is calculated based on the steady-state probability,and the joint optimization algorithm of spare parts inventory allocation and the redundancy level is used to solve the model.Finally,the correctness of the availability model is validated and the validity of the joint optimization is verified by numerical calculation.Through the numerical calculation results,it is shown that the proposed availability model is an improvement of the traditional model and processes the universality.The joint optimization results show that the redundancy system availability increases with the increase of the redundancy level and the spare parts inventory.However,further improvement of availability will lead to a sharp increase in cost when it is close to 1.The proportion of spare parts inventory cost is the highest in the life cycle cost,while the spare parts ordering cost is the lowest.Compared with the method that only considers spare parts inventory optimization,the life cycle cost of the joint optimization method is reduced by 8.01%.
引文
[1]XIE W,LIAO H,JIN T.Maximizing system availability through joint decision on component redundancy and spares inventory[J].European Journal of Operational Research,2014,237(1):164-176.
[2]SHERBROOKE C C.METRIC:A multi-echelon technique for recoverable item control[J].Operations Research,1968,16(1):122-141.
[3]MUCKSTADTJ A.A model for a multi-item,multi-echelon,multi-indenture inventory system[J].Management Science,1973,20(4):472-481.
[4]COCHRANJ K,LEWIST P.Computing small-fleet aircraft availabilities including redundancy and spares[J].Computers&Operations Research,2002,29(5):529-540.
[5]AXSATER S,HOWARD C,MARKLUND J.A distribution inventory model with transshipments from a support warehouse[J].IIETransactions,2013,45(3):309-322.
[6]COSTANTINO F,DI GRAVIO G,TRONCI M.Multi-echelon,multi-indenture spare parts inventory control subject to system availability and budget constraints[J].Reliability Engineering&System Safety,2013,119(119):95-101.
[7]DE SMIDT-DESTOMBES K S,VAN DER HEIJDEN M C,VAN HARTEN A.On the interaction between maintenance,spare part inventories and repair capacity for a k-out-of-Nsystem with wear-out[J].European Journal of Operational Research,2006,174(1):182-200.
[8]DE SMIDT-DESTOMBES K S,VAN ELST N P,BARROS AI,et al.A spare parts model with cold-standby redundancy on system level[J].Computers&Operations Research,2011,38(7):985-991
[9]CHAKRAVARTHY S R,GMEZ-CORRAL A.The influence of delivery times on repairable k-out-of-Nsystems with spares[J].Applied Mathematical Modelling,2009,33(5):2368-2387.
[10]VAN JAARSVELD W,DEKKER R.Spare parts stock control for redundant systems using reliability centered maintenance data[J].Reliability Engineering&System Safety,2011,96(11):1576-1586.
[11]BJARNASON E T S,TAGHIPOUR S,BANJEVIC D.Joint optimal inspection and inventory for a k-out-of-N system[J].Reliability Engineering&System Safety,2014,131:203-215.
[12]ONER K B,KIESMLLER G P,VAN HOUTUM G J.Optimization of component reliability in the design phase of capital goods[J].European Journal of Operational Research,2010,205(3):615-624.
[13]SLEPTCHENKO A,VAN DER HEIJDEN M.Joint optimization of redundancy level and spare part inventories[J].Reliability Engineering&System Safety,2016,153:64-74.
[14]JIN T,TABOADA H,ESPIRITU J,et al.Allocation of reliability-redundancy and spares inventory under Poisson fleet expansion[J].IISE Transactions,2017,49(7):737-751.
[15]SELCUK B,AGRALI S.Joint spare parts inventory and reliability decisions under a service constraint[J].Journal of the Operational Research Society,2013,64(3):446-458.
[16]MOGHADDASSR,ZUOM J.Optimal design of a repairable k-out-of-N system considering maintenance[C]∥Proc.of the Reliability and Maintainability Symposium,2011:1-6.
[17]卢雷,杨江平.k/N(G)结构系统初始备件配置方法[J].航空学报,2014,35(3):773-779.LU L,YANG J P.Initial spare allocation method for k/N(G)structure system[J].Acta Aeronautica et Astronautica Sinica,2014,35(3):773-779.
[18]FAWZI B B,HAWKES A G.Availability of an R-out-ofNsystem with spares and repairs[J].Journal of applied probability,1991,28(2):397-408.
[19]FROSTIG E,LEVIKSON B.On the availability of Rout of Nrepairable systems[J].Naval Research Logistics,2002,49(5):483-498.
[20]DE SMIDT-DESTOMBES K S,VAN DER HEIJDEN M C,VAN HARTEN A.On the availability of a k-out-of-Nsystem given limited spares and repair capacity under a condition based maintenance strategy[J].Reliability Engineering&System Safety,2004,83(3):287-300.
[21]CEKYAY B,OZEKICI S.Reliability,MTTF and steadystate availability analysis of systems with exponential lifetimes[J].Applied Mathematical Modelling,2015,39(1):284-296.
[22]MOGHADDASS R,ZUO M J,QU J.Reliability and availability analysis of a repairable k-out-of-N:gsystem with rrepairmen subject to shut-off rules[J].IEEE Trans.on Reliability,2011,60(3):658-666.
[2]SHERBROOKE C C.METRIC:A multi-echelon technique for recoverable item control[J].Operations Research,1968,16(1):122-141.
[3]MUCKSTADTJ A.A model for a multi-item,multi-echelon,multi-indenture inventory system[J].Management Science,1973,20(4):472-481.
[4]COCHRANJ K,LEWIST P.Computing small-fleet aircraft availabilities including redundancy and spares[J].Computers&Operations Research,2002,29(5):529-540.
[5]AXSATER S,HOWARD C,MARKLUND J.A distribution inventory model with transshipments from a support warehouse[J].IIETransactions,2013,45(3):309-322.
[6]COSTANTINO F,DI GRAVIO G,TRONCI M.Multi-echelon,multi-indenture spare parts inventory control subject to system availability and budget constraints[J].Reliability Engineering&System Safety,2013,119(119):95-101.
[7]DE SMIDT-DESTOMBES K S,VAN DER HEIJDEN M C,VAN HARTEN A.On the interaction between maintenance,spare part inventories and repair capacity for a k-out-of-Nsystem with wear-out[J].European Journal of Operational Research,2006,174(1):182-200.
[8]DE SMIDT-DESTOMBES K S,VAN ELST N P,BARROS AI,et al.A spare parts model with cold-standby redundancy on system level[J].Computers&Operations Research,2011,38(7):985-991
[9]CHAKRAVARTHY S R,GMEZ-CORRAL A.The influence of delivery times on repairable k-out-of-Nsystems with spares[J].Applied Mathematical Modelling,2009,33(5):2368-2387.
[10]VAN JAARSVELD W,DEKKER R.Spare parts stock control for redundant systems using reliability centered maintenance data[J].Reliability Engineering&System Safety,2011,96(11):1576-1586.
[11]BJARNASON E T S,TAGHIPOUR S,BANJEVIC D.Joint optimal inspection and inventory for a k-out-of-N system[J].Reliability Engineering&System Safety,2014,131:203-215.
[12]ONER K B,KIESMLLER G P,VAN HOUTUM G J.Optimization of component reliability in the design phase of capital goods[J].European Journal of Operational Research,2010,205(3):615-624.
[13]SLEPTCHENKO A,VAN DER HEIJDEN M.Joint optimization of redundancy level and spare part inventories[J].Reliability Engineering&System Safety,2016,153:64-74.
[14]JIN T,TABOADA H,ESPIRITU J,et al.Allocation of reliability-redundancy and spares inventory under Poisson fleet expansion[J].IISE Transactions,2017,49(7):737-751.
[15]SELCUK B,AGRALI S.Joint spare parts inventory and reliability decisions under a service constraint[J].Journal of the Operational Research Society,2013,64(3):446-458.
[16]MOGHADDASSR,ZUOM J.Optimal design of a repairable k-out-of-N system considering maintenance[C]∥Proc.of the Reliability and Maintainability Symposium,2011:1-6.
[17]卢雷,杨江平.k/N(G)结构系统初始备件配置方法[J].航空学报,2014,35(3):773-779.LU L,YANG J P.Initial spare allocation method for k/N(G)structure system[J].Acta Aeronautica et Astronautica Sinica,2014,35(3):773-779.
[18]FAWZI B B,HAWKES A G.Availability of an R-out-ofNsystem with spares and repairs[J].Journal of applied probability,1991,28(2):397-408.
[19]FROSTIG E,LEVIKSON B.On the availability of Rout of Nrepairable systems[J].Naval Research Logistics,2002,49(5):483-498.
[20]DE SMIDT-DESTOMBES K S,VAN DER HEIJDEN M C,VAN HARTEN A.On the availability of a k-out-of-Nsystem given limited spares and repair capacity under a condition based maintenance strategy[J].Reliability Engineering&System Safety,2004,83(3):287-300.
[21]CEKYAY B,OZEKICI S.Reliability,MTTF and steadystate availability analysis of systems with exponential lifetimes[J].Applied Mathematical Modelling,2015,39(1):284-296.
[22]MOGHADDASS R,ZUO M J,QU J.Reliability and availability analysis of a repairable k-out-of-N:gsystem with rrepairmen subject to shut-off rules[J].IEEE Trans.on Reliability,2011,60(3):658-666.
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