考虑备件及维修周转的并串混联系统可用度模型
|
摘要
给出了综合考虑系统结构、库存备件量和故障件维修周转等因素影响下的系统可用度计算模型。将由并串混联系统和备件组成的广义系统按功能划分为工作系统与库存系统两个子系统,通过引入备件平均到达率反映库存系统对工作系统的影响,并据此分别建立备件充足与缺货时的工作系统状态转移关系。利用二项分布表征期望备件短缺数的概率分布函数以计算库存系统备件的缺货概率,进而根据全概率公式计算得到系统可用度。示例表明:所提模型针对单部件串联系统所得结果比已有模型更为精确;其次,在库存备件量及维修周转时间的影响下,多部件子系统串联时并不比单部件串联时的可用度高,且可用度曲线随着库存量的增加并不是严格单调递增的凸曲线。
Availability modeling of parallel-series system is proposed with the consideration of system structure,the number of spare parts,and maintenance turnover.Therefore,the whole system composed of parallelseries system and spare parts is divided into operation system and inventory system according to its function.By introducing the average rate of arrival of spare parts to reflect the influence of the inventory system on the operation system,state transfer relationship of the operation system is given under the conditions that spare parts are sufficient and insufficient.And the binomial distribution is used as the probability distribution function of expected backorder to calculate spares shortage probability's,further to calculate system availability with the formula of full probability.Ultimately,the example shows that,firstly,aiming at series system,the results of the proposed model is better than those of the former model;secondly,under the influence of the number of spare parts and maintenance turnover,availability of multi 1/Nsystem is not higher than series system and the availability curve is not strictly monotonically increasing convex curve with the increase of inventory.
Availability modeling of parallel-series system is proposed with the consideration of system structure,the number of spare parts,and maintenance turnover.Therefore,the whole system composed of parallelseries system and spare parts is divided into operation system and inventory system according to its function.By introducing the average rate of arrival of spare parts to reflect the influence of the inventory system on the operation system,state transfer relationship of the operation system is given under the conditions that spare parts are sufficient and insufficient.And the binomial distribution is used as the probability distribution function of expected backorder to calculate spares shortage probability's,further to calculate system availability with the formula of full probability.Ultimately,the example shows that,firstly,aiming at series system,the results of the proposed model is better than those of the former model;secondly,under the influence of the number of spare parts and maintenance turnover,availability of multi 1/Nsystem is not higher than series system and the availability curve is not strictly monotonically increasing convex curve with the increase of inventory.
引文
[1]殷鹤龄.可靠性维修性保障性术语集[M].北京:国防工业出版社,2002:29-30.YIN H L.Reliability,maintainability and supportability terms[M].Beijing:National Defence Industry Press,2002:29-30.
[2]曹晋华,程侃.可靠性数学引论[M].2版.北京:高等教育出版社,2012:224-225.CAO J H,CHENG K.Introduction to mathematical reliability[M].2nd ed.Beijing:Higher Education Press,2012:224-225.
[3]FAWZI B B,HAWKES A G.Availability of an r-out-of-Nsystem with spares and repairs[J].Journal of Applied Probability,1991,28(2):397-408.
[4]FROSTIG E,LEVIKSON B.On the availability of r-out-of-N repairable systems[J].Naval Research Logistics(NRL),2002,49(5):483-498.
[5]SMITH M A J,DEKKER R.Preventive maintenance in a 1-out-of-N system:the uptime,downtime and costs[J].European Journal of Operational Research,1997,99(3):565-583.
[6]DE SMIDT-DESTOMBES K S,C VAN DER HEIJDEN M,VAN HARTEN A.On the availability of a k-out-of-N system given limited spares and repair capacity under a condition based maintenance strategy[J].Reliability Engineering&System Safety,2004,83(3):287-300.
[7]张涛,郭波,武小悦,等.任意结构系统的备件可用度评估模型[J].航空学报,2005,26(2):203-207.ZHANG T,GUO B,WU X Y,et al.Spare availability model for system with various configurations[J].Acta Aeronoutica et Astronautica Sinica,2005,26(2):203-207.
[8]WU X,HILLSTON J,FENG C.Availability modeling of generalized k-out-of-N:G warm standby systems with PEPA[J].IEEE Trans.on Systems Man&Cybernetics Systems,2016,PP(99):1-12.
[9]FAGHIH-ROOHI S,XIE M,NG K M,et al.Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-Nsystems[J].Reliability Engineering&System Safety,2014,123(4):57-62.
[10]SHERBROOKE C C.Metric:a multi-echelon technique for recoverable item control[J].Operations Research,1968,16(1):122-141.
[11]SHERBROOKE C C.VARI-METRIC:improved approximations for multi-indenture,multi-echelon availability models[J].Operations Research,1986,34(2):311-319.
[12]GRAVES S C.A multi-echelon inventory model for a repairable item with one-for-one replenishment[J].Management Science,2011,31(10):1247-1256.
[13]ALFREDSSON P.Optimization of multi-echelon repairable item inventory systems with simultaneous location of repair facilities[J].European Journal of Operational Research,1997,99(3):584-595.
[14]ALFREDSSON P,VERRIJDT J.Modeling emergency supply flexibility in a two-echelon inventory system[J].Management Science,1999,45(10):1416-1431.
[15]MUCKSTAD J A.A model for a multi-item,multi-echelon,multi-indenture inventory system[J].Management Science,1973,20(4-Part-I):472-481.
[16]SMIDT-DESTOMBESA K S D,HARTEN A V.On the interaction between maintenance,spare part inventories and repair capacity for a k-out-of-N system with wear-out[J].European Journal of Operational Research,2006,174(1):182-200.
[17]DE SMIDT-DESTOMBES K S,VAN DER HEIJDEN M C,VAN HARTEN A.Availability of k-out-of-N systems under block replacement sharing limited spares and repair capacity[J].International Journal of Production Economics,2007,107(2):404-421.
[18]ZHANG T,XIE M,HORIGOME M.Availability and reliability of k-out-of-(M+N):G warm standby systems[J].Reliability Engineering&System Safety,2006,91(4):381-387.
[19]刘勇,武昌,李阳,等.两级备件保障系统的装备时变可用度评估模型[J].兵工学报,2010,31(2):253-256.LIU Y,WU C,LI Y,et al.Evaluation model of equipment time-varying availability in two-echelon spare support system[J].Journal of Acta Armamentarii,2010,31(2):253-256.
[20]艾宝利,武昌.两级维修保障下k/N系统使用可用度模型[J].系统工程学报,2011,26(3):421-426.AI B L,WU C.Operational availability model for k/Nsystem under two grade maintenance support policy[J].Journal of Systems Engineering,2011,26(3):421-426.
[21]PEDRAM S,BARIS B,DRAGAN B.Spare parts provisioning for multiple k-out-of-N:G systems[J].IIE Transactions,2013,45(9):953-963.
[22]张涛,武小悦,郭波,等.(m,Ng)维修策略下可修系统的使用可用度模型[J].系统工程学报,2007,22(6):24-24.ZHANG T,WU X Y,GUO B,et al.Repairable system operational availability model under(m,Ng)maintenance strategy[J].Journal of Systems Engineering,2007,22(6):24-24.
[23]刘宝慧.维修时间服从伽玛分布的k/N系统在(n,r,r)维修策略下的可用度[J].青海大学学报,2008,26(6):61-64.LIU B H.The operational availability of a k/Nsystem with the maintenance time submitted to gamma distribution under(n,r,r)maintenance strategy[J].Journal of Qinghai University,2008,26(6):61-64.
[24]贾秀芹,刘瑞元.k/N系统在(n,L,r,r)维修策略下的可用度[J].西南大学学报(自然科学版),2011,33(9):17-21.JIA X Q,LIU R Y.Availability for the k-out-of-Nsystem under(n,L,r,r)maintenance policy[J].Journal of Southwest University,2011,33(9):17-21.
[25]KHATAB A,NAHAS N,NOURELFATH M.Availability of k-out-of-N:G,systems with non-identical components subject to repair priorities[J].Reliability Engineering&System Safety,2009,94(2):142-151.
[26]KNEZEVIC A,VASOV L,VLACIC S,et al.Imperfect maintenance model for estimating aircraft fleet availability[J].Aircraft Engineering&Aerospace Technology,2017,89(2):338-346.
[27]ALASWAD S,RICHARD C,POHL E A.A model of system limiting availability under imperfect maintenance[J].Journal of Quality in Maintenance Engineering,2017,23(3).DOI:10.1108/JQME-06-2016-0024.
[28]KE J C,YANG D Y,SHEU S H,et al.Availability of a repairable retrial system with warm standby components[J].International Journal of Computer Mathematics,2013,90(11):2279-2297.
[29]LI X,HE R,YAN Z,et al.A new imperfect maintenance model based on delay-time concepts for single components with multiple failure modes[J].International Journal of System Assurance Engineering&Management,2015,6(4):479-486.
[30]KEIZER M C A O,TEUNTER R H,VELDMAN J.Clustering condition-based maintenance for systems with redundancy and economic dependencies[J].European Journal of Operational Research,2016,251(2):531-540.
[31]ABDELBAR K M,BOUAMI D,ELFEZAZI S.Improvement maintenance implementation based on downtime analysis approach[J].Journal of Quality in Maintenance Engineering,2016,22(4):378-393.
[32]王蕴,王乃超,马麟,等.考虑备件约束的多部件串联系统使用可用度计算方法[J].航空学报,2015,36(4):1195-1201.WANG Y,WANG N C,MA L,et al.Operational availability calculation methods of various series system under the constraint of spare parts[J].Acta Aeronautica et Astronautica Sinica,2015,36(4):1195-1201.
[33]LITTLE J D C,Graves S C.Little's law[M].New York:Springer,2008:81-100.
[2]曹晋华,程侃.可靠性数学引论[M].2版.北京:高等教育出版社,2012:224-225.CAO J H,CHENG K.Introduction to mathematical reliability[M].2nd ed.Beijing:Higher Education Press,2012:224-225.
[3]FAWZI B B,HAWKES A G.Availability of an r-out-of-Nsystem with spares and repairs[J].Journal of Applied Probability,1991,28(2):397-408.
[4]FROSTIG E,LEVIKSON B.On the availability of r-out-of-N repairable systems[J].Naval Research Logistics(NRL),2002,49(5):483-498.
[5]SMITH M A J,DEKKER R.Preventive maintenance in a 1-out-of-N system:the uptime,downtime and costs[J].European Journal of Operational Research,1997,99(3):565-583.
[6]DE SMIDT-DESTOMBES K S,C VAN DER HEIJDEN M,VAN HARTEN A.On the availability of a k-out-of-N system given limited spares and repair capacity under a condition based maintenance strategy[J].Reliability Engineering&System Safety,2004,83(3):287-300.
[7]张涛,郭波,武小悦,等.任意结构系统的备件可用度评估模型[J].航空学报,2005,26(2):203-207.ZHANG T,GUO B,WU X Y,et al.Spare availability model for system with various configurations[J].Acta Aeronoutica et Astronautica Sinica,2005,26(2):203-207.
[8]WU X,HILLSTON J,FENG C.Availability modeling of generalized k-out-of-N:G warm standby systems with PEPA[J].IEEE Trans.on Systems Man&Cybernetics Systems,2016,PP(99):1-12.
[9]FAGHIH-ROOHI S,XIE M,NG K M,et al.Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-Nsystems[J].Reliability Engineering&System Safety,2014,123(4):57-62.
[10]SHERBROOKE C C.Metric:a multi-echelon technique for recoverable item control[J].Operations Research,1968,16(1):122-141.
[11]SHERBROOKE C C.VARI-METRIC:improved approximations for multi-indenture,multi-echelon availability models[J].Operations Research,1986,34(2):311-319.
[12]GRAVES S C.A multi-echelon inventory model for a repairable item with one-for-one replenishment[J].Management Science,2011,31(10):1247-1256.
[13]ALFREDSSON P.Optimization of multi-echelon repairable item inventory systems with simultaneous location of repair facilities[J].European Journal of Operational Research,1997,99(3):584-595.
[14]ALFREDSSON P,VERRIJDT J.Modeling emergency supply flexibility in a two-echelon inventory system[J].Management Science,1999,45(10):1416-1431.
[15]MUCKSTAD J A.A model for a multi-item,multi-echelon,multi-indenture inventory system[J].Management Science,1973,20(4-Part-I):472-481.
[16]SMIDT-DESTOMBESA K S D,HARTEN A V.On the interaction between maintenance,spare part inventories and repair capacity for a k-out-of-N system with wear-out[J].European Journal of Operational Research,2006,174(1):182-200.
[17]DE SMIDT-DESTOMBES K S,VAN DER HEIJDEN M C,VAN HARTEN A.Availability of k-out-of-N systems under block replacement sharing limited spares and repair capacity[J].International Journal of Production Economics,2007,107(2):404-421.
[18]ZHANG T,XIE M,HORIGOME M.Availability and reliability of k-out-of-(M+N):G warm standby systems[J].Reliability Engineering&System Safety,2006,91(4):381-387.
[19]刘勇,武昌,李阳,等.两级备件保障系统的装备时变可用度评估模型[J].兵工学报,2010,31(2):253-256.LIU Y,WU C,LI Y,et al.Evaluation model of equipment time-varying availability in two-echelon spare support system[J].Journal of Acta Armamentarii,2010,31(2):253-256.
[20]艾宝利,武昌.两级维修保障下k/N系统使用可用度模型[J].系统工程学报,2011,26(3):421-426.AI B L,WU C.Operational availability model for k/Nsystem under two grade maintenance support policy[J].Journal of Systems Engineering,2011,26(3):421-426.
[21]PEDRAM S,BARIS B,DRAGAN B.Spare parts provisioning for multiple k-out-of-N:G systems[J].IIE Transactions,2013,45(9):953-963.
[22]张涛,武小悦,郭波,等.(m,Ng)维修策略下可修系统的使用可用度模型[J].系统工程学报,2007,22(6):24-24.ZHANG T,WU X Y,GUO B,et al.Repairable system operational availability model under(m,Ng)maintenance strategy[J].Journal of Systems Engineering,2007,22(6):24-24.
[23]刘宝慧.维修时间服从伽玛分布的k/N系统在(n,r,r)维修策略下的可用度[J].青海大学学报,2008,26(6):61-64.LIU B H.The operational availability of a k/Nsystem with the maintenance time submitted to gamma distribution under(n,r,r)maintenance strategy[J].Journal of Qinghai University,2008,26(6):61-64.
[24]贾秀芹,刘瑞元.k/N系统在(n,L,r,r)维修策略下的可用度[J].西南大学学报(自然科学版),2011,33(9):17-21.JIA X Q,LIU R Y.Availability for the k-out-of-Nsystem under(n,L,r,r)maintenance policy[J].Journal of Southwest University,2011,33(9):17-21.
[25]KHATAB A,NAHAS N,NOURELFATH M.Availability of k-out-of-N:G,systems with non-identical components subject to repair priorities[J].Reliability Engineering&System Safety,2009,94(2):142-151.
[26]KNEZEVIC A,VASOV L,VLACIC S,et al.Imperfect maintenance model for estimating aircraft fleet availability[J].Aircraft Engineering&Aerospace Technology,2017,89(2):338-346.
[27]ALASWAD S,RICHARD C,POHL E A.A model of system limiting availability under imperfect maintenance[J].Journal of Quality in Maintenance Engineering,2017,23(3).DOI:10.1108/JQME-06-2016-0024.
[28]KE J C,YANG D Y,SHEU S H,et al.Availability of a repairable retrial system with warm standby components[J].International Journal of Computer Mathematics,2013,90(11):2279-2297.
[29]LI X,HE R,YAN Z,et al.A new imperfect maintenance model based on delay-time concepts for single components with multiple failure modes[J].International Journal of System Assurance Engineering&Management,2015,6(4):479-486.
[30]KEIZER M C A O,TEUNTER R H,VELDMAN J.Clustering condition-based maintenance for systems with redundancy and economic dependencies[J].European Journal of Operational Research,2016,251(2):531-540.
[31]ABDELBAR K M,BOUAMI D,ELFEZAZI S.Improvement maintenance implementation based on downtime analysis approach[J].Journal of Quality in Maintenance Engineering,2016,22(4):378-393.
[32]王蕴,王乃超,马麟,等.考虑备件约束的多部件串联系统使用可用度计算方法[J].航空学报,2015,36(4):1195-1201.WANG Y,WANG N C,MA L,et al.Operational availability calculation methods of various series system under the constraint of spare parts[J].Acta Aeronautica et Astronautica Sinica,2015,36(4):1195-1201.
[33]LITTLE J D C,Graves S C.Little's law[M].New York:Springer,2008:81-100.