修理设备可修且部件修复非新的温贮备可修系统
|
摘要
分析了温贮备可修系统的又一个新模型,引入了修理设备可修这一概念,即修理设备工作期间发生故障时,先对其进行修理,当修理设备修复后,继续投入使用中。同时考虑修理工多重休假的情形,进一步对两部件组成的修复非新的温贮备可修系统研究。假定部件1的工作时间、贮备时间,部件2的工作时间、贮备时间及修理设备的寿命均服从指数分布,部件2的修理时间、修理工休假时间及修理设备的修理时间均服从一般连续型分布,利用补充变量法将其扩充为广义Markov过程,建立各状态概率的微分方程,并应用Laplace变换及其反演,得到系统主要可靠性指标。
A new model of warm fund maintenance system is analyzed,and the concept of repairable repair equipment is introduced,which means repair equipment can repair itself during working and continue to put into using. At the same time,considering the situation of repairman with multiple vacations,the two part of the new non warm standby repairable system is studied. It is assumed that the working time,standby time of part 1,and the working time,standby time and repair equipment life of part 2 obey the exponential distribution; the repair time,the repairman vacation time and repair equipment repair time of part 2 obey the general distribution. By using the supplementary variable method,which is extended to generalized Markov process,differential equations for the state probabilities is established,and the main system reliability index is obtained by the application of Laplasse transform and its inversion.
A new model of warm fund maintenance system is analyzed,and the concept of repairable repair equipment is introduced,which means repair equipment can repair itself during working and continue to put into using. At the same time,considering the situation of repairman with multiple vacations,the two part of the new non warm standby repairable system is studied. It is assumed that the working time,standby time of part 1,and the working time,standby time and repair equipment life of part 2 obey the exponential distribution; the repair time,the repairman vacation time and repair equipment repair time of part 2 obey the general distribution. By using the supplementary variable method,which is extended to generalized Markov process,differential equations for the state probabilities is established,and the main system reliability index is obtained by the application of Laplasse transform and its inversion.
引文
[1]曹晋华,程侃.可靠性数学引论[M].2版.北京:高等教育出版社,2006.
[2]程侃.寿命分布类与可靠性数学引论[M].北京:科学出版社,1999.
[3]汪军芳,张民悦.两个相依部件并联系统和有冷贮备部件串联系统的模糊可靠性[J].四川理工学院学报:自然科学版,2015,28(1):80-82.
[4]梁丽丹.n个同型部件和k个修理设备的并联可修系统的可靠度探究[J].四川理工学院学报:自然科学版,2016,29(4):88-93.
[5]张民悦,邬一凡.具有多重休假开关连续型温贮备可修系统的可靠性分析[J].兰州理工大学学报,2015,41(5):152-156.
[6]YUAN L,MENG X Y.Reliability analysis of a warm standby repairable system with priority in use[J].Applied Mathematical Modelling,2011,35(9):4295-4303.
[7]程江,唐应辉.修理设备可更换的三部件串-并联可修系统的可靠性分析[J].西南大学学报:自然科学版,2010,32(1):148-154.
[8]姜颖,唐应辉.部件有两类故障状态且修理设备可更换的并联可修系统分析[J].应用数学,2014,27(3):535-545.
[9]CAO J H,WU Y H.Reliability analysis of a multistate system with a replaceable repair facility[J].Acta Math Appl Sinica,1988,4(2):113-121.
[10]吴文青,唐应辉,姜颖.修理工多重休假且修理设备可更换的k/n(G)表决可修系统研究[J].系统工程理论与实践,2013,33(10):2604-2614.
[11]张欣欣,孟宪云,陈胜强,等.修理设备可更换且修理工多重延误休假的温贮备系统[J].郑州大学学报:理学版,2013,45(3):13-18.
[12]刘仁彬,唐应辉.修理设备可更换且修理有延误的两不同部件并联可修系统[J].高校应用数学学报,2006,21(2):127-140.
[13]刘海涛,孟宪云.具有单重休假和修复不如新的两部件温贮备系统[J].自动化学报,2012,38(4):639-646.
[14]吕文静,郑海鹰.修理工可延误休假且部件不能修复如新的温贮备可修系统[J].浙江大学学报:理学版,2014,41(5):512-517.
[15]史定华.计算可修系统在(0,t]中平均故障次数的新方法[J].应用数学学报,1985,8(1):101-110.
[16]张民悦,姜明明.开关寿命连续型三不同型部件温贮备可修系统可靠性分析[J].四川理工学院学报:自然科学版,2015,28(6):87-91.
[17]张民悦,连爱玲.开关寿命连续型且部件修复非新的温贮备可修系统[J].四川理工学院学报:自然科学版,2017,30(2):90-97.
[18]张民悦,黄鹏远.延迟修理的三失效状态可修系统的最优更换模型[J].系统科学与数学,2016,36(1):134-144.
[2]程侃.寿命分布类与可靠性数学引论[M].北京:科学出版社,1999.
[3]汪军芳,张民悦.两个相依部件并联系统和有冷贮备部件串联系统的模糊可靠性[J].四川理工学院学报:自然科学版,2015,28(1):80-82.
[4]梁丽丹.n个同型部件和k个修理设备的并联可修系统的可靠度探究[J].四川理工学院学报:自然科学版,2016,29(4):88-93.
[5]张民悦,邬一凡.具有多重休假开关连续型温贮备可修系统的可靠性分析[J].兰州理工大学学报,2015,41(5):152-156.
[6]YUAN L,MENG X Y.Reliability analysis of a warm standby repairable system with priority in use[J].Applied Mathematical Modelling,2011,35(9):4295-4303.
[7]程江,唐应辉.修理设备可更换的三部件串-并联可修系统的可靠性分析[J].西南大学学报:自然科学版,2010,32(1):148-154.
[8]姜颖,唐应辉.部件有两类故障状态且修理设备可更换的并联可修系统分析[J].应用数学,2014,27(3):535-545.
[9]CAO J H,WU Y H.Reliability analysis of a multistate system with a replaceable repair facility[J].Acta Math Appl Sinica,1988,4(2):113-121.
[10]吴文青,唐应辉,姜颖.修理工多重休假且修理设备可更换的k/n(G)表决可修系统研究[J].系统工程理论与实践,2013,33(10):2604-2614.
[11]张欣欣,孟宪云,陈胜强,等.修理设备可更换且修理工多重延误休假的温贮备系统[J].郑州大学学报:理学版,2013,45(3):13-18.
[12]刘仁彬,唐应辉.修理设备可更换且修理有延误的两不同部件并联可修系统[J].高校应用数学学报,2006,21(2):127-140.
[13]刘海涛,孟宪云.具有单重休假和修复不如新的两部件温贮备系统[J].自动化学报,2012,38(4):639-646.
[14]吕文静,郑海鹰.修理工可延误休假且部件不能修复如新的温贮备可修系统[J].浙江大学学报:理学版,2014,41(5):512-517.
[15]史定华.计算可修系统在(0,t]中平均故障次数的新方法[J].应用数学学报,1985,8(1):101-110.
[16]张民悦,姜明明.开关寿命连续型三不同型部件温贮备可修系统可靠性分析[J].四川理工学院学报:自然科学版,2015,28(6):87-91.
[17]张民悦,连爱玲.开关寿命连续型且部件修复非新的温贮备可修系统[J].四川理工学院学报:自然科学版,2017,30(2):90-97.
[18]张民悦,黄鹏远.延迟修理的三失效状态可修系统的最优更换模型[J].系统科学与数学,2016,36(1):134-144.