TY - JOUR AU - Zhang, Xiao AU - Guo, Lina PY - 2015 TI - A new kind of repairable system with repairman vacations JO - Journal of Nonlinear Sciences and Applications SP - 324--333 VL - 8 IS - 4 AB - In this paper, a new kind of series repairable system with repairman vacation is discussed, in which the failure rate functions of all the units and the delayed vacation rate function of the repairman are related to the working time of the system. The system model of a group of integro-differential equations is established by using probability analysis method, which then is translated into an initial value problem of a class of abstract semi-linear evolution equation in a suitable Banach space for further study. Then the conditions of the existence and uniqueness of the system solution is analyzed by using \(C_0\)-semigroup theory. And by using Laplace transform method, some steady-state reliability indexes, such as system availability, failure frequency, and the probability that the repairman is on vacation, are discussed. Numerical examples are also presented at the end of the paper. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.008.04.05 DO - 10.22436/jnsa.008.04.05 ID - Zhang2015 ER - TY - BOOK TI - Introduction to reliability mathematics AU - J. H. Cao AU - K. Cheng PB - Higher education press PY - 1986 DA - 1986// CY - Beijing ID - Cao1986 ER - TY - JOUR TI - Stability analysis of a new kind n-unit series repairable system AU - L. N. Guo AU - H. B. Xu AU - C. Gao AU - G. T. Zhu JO - Appl. Math. Model. PY - 2011 DA - 2011// VL - 35 ID - Guo2011 ER - TY - JOUR TI - Bilevel control of degraded machining system with warm standbys, setup and vacation AU - M. Jain AU - Rakhee AU - M. Singh JO - Appl. Math. Model. PY - 2004 DA - 2004// VL - 28 ID - Jain2004 ER - TY - JOUR TI - A replacement policy for a repairable system with its repairman having multiple vacations AU - J. S. Jia AU - S. M. Wu JO - Comput. Ind. Eng. PY - 2009 DA - 2009// VL - 57 ID - Jia2009 ER - TY - JOUR TI - Vacation policies for machine repair problem with two type spares AU - J. C. Ke AU - K. H. Wang JO - Appl. Math. Model. PY - 2007 DA - 2007// VL - 31 ID - Ke2007 ER - TY - JOUR TI - The positive solutions of abstract semilinear evolution equations and their applications AU - Y. X. Li JO - Acta Math. Sinica PY - 1996 DA - 1996// VL - 39 ID - Li 1996 ER - TY - JOUR TI - Existence and uniqueness of positive periodic solutions for abstract semilinear evolution equations AU - Y. X. Li JO - J. Syst. Sci. Math. Sci. PY - 2005 DA - 2005// VL - 28 ID - Li 2005 ER - TY - JOUR TI - Existence of Solutions of Initial Value Problems for Abstract Semilinear Evolution Equations AU - Y. X. Li JO - Acta Math. Sinica PY - 2005 DA - 2005// VL - 48 ID - Li 2005 ER - TY - JOUR TI - One-unit repairable system with multiple delay vacations AU - R. B. Liu AU - Y. H. Tang JO - Chinese J. Eng. Math. PY - 2006 DA - 2006// VL - 23 ID - Liu2006 ER - TY - JOUR TI - Reliability analysis of a two-dissimilar-unit cold standby system with separated repair rule AU - R. B. Liu AU - Y. H. Tang JO - J. Syst. Eng. PY - 2006 DA - 2006// VL - 21 ID - Liu2006 ER - TY - JOUR TI - A new kind of N-unit series repairable system and its reliability analysis AU - R. B. Liu AU - Y. H. Tang AU - C. Y. Luo JO - Math. Appl. PY - 2007 DA - 2007// VL - 20 ID - Liu2007 ER - TY - BOOK TI - Semigroups of linear operators and applicaton to partial differential equations AU - A. Pazy PB - Springer-Verlag PY - 1983 DA - 1983// CY - New York ID - Pazy1983 ER - TY - BOOK TI - Studies of some aspects on abstract semilinear evolution solutions and functional differential equations AU - L. L. Wang PB - College of Mathematics and Econometrics PY - 2001 DA - 2001// CY - Hunan University ID - Wang2001 ER - TY - JOUR TI - Reliability analysis of two-unit cold standby repairable systems under Poisson shocks AU - Q. T. Wu AU - S. M. Wu JO - Appl. Math. Comput. PY - 2011 DA - 2011// VL - 218 ID - Wu2011 ER - TY - JOUR TI - A deteriorating system with its repairman having multiple vacations AU - L. Yuan AU - J. Xu JO - Appl. Math. Comput. PY - 2011 DA - 2011// VL - 217 ID - Yuan2011 ER -