Stability analysis of a new kind n-unit series repairable system |
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Authors: | Lina Guo Houbao Xu Chao Gao Guangtian Zhu |
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Affiliation: | 1. Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China;2. Department of System Engineering, Beijing Institute of Information and Control, Beijing 100037, China;3. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China;4. Department of Mathematics, Yanbian University, Yanji 133002, China;5. Academy of Mathematics and System Sciences, C.A.S., Beijing 100080, China |
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Abstract: | In this paper, we deal with a new model of an n-unit series repairable system, in which a concept of a repairman with multiple-delayed vacation is introduced and the impact on the system reliability due to a replaceable facility is also considered. This paper is devoted to studying the unique existence and stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system in a special case. Some reliability indices of the system are also studied and the optimal vacation time is analyzed at the end of the paper. |
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Keywords: | Availability C0-semigroup theory Asymptotic stability Steady-state solution Reliability indices |
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