Well Posedness and Optimal Check Time of a Repairable System
XU Houbao(1),LIU Helong(2), ZHU Guangtian(3)
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(1)Beijing Institute of Technology, Beijing 100081;(2)Xinyang Normal University, Xinyang 464000;(3)Academy of Mathematics and Systems Science, Beijing 100080
The existence of optimal check time of a repairable system with repair time following general distribution is studied. First, the unique existence of the solution of such system is proved. Then, by the positive -semigroup generated by system operator, it is shown that there exists a steady nonnegative solution of the system which is just the normalized eigenvector corresponding to eigenvalue 0 of system operator. At last, based on steady availability of the system, the existence of optimal check time is given.
XU Houbao
, LIU Helong
, ZHU Guangtian. , {{custom_author.name_en}}.
Well Posedness and Optimal Check Time of a Repairable System. Journal of Systems Science and Mathematical Sciences, 2008, 28(3): 265-274 https://doi.org/10.12341/jssms10066