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Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 53-314
Full Name: WENZHI YUAN
Position: Assistant Professor
Age: ON
Sex: Male
Address: Taiyuan Teachers College
Country: CHINA
Tel: 15022132945,13934233255
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E-mail address: ywzywz123@163.com
Other E-mails: wzyuan123@yahoo.cn
Title of the Paper: Spectral analysis of a two unit deteriorating standby system with repair
Authors as they appear in the Paper: WENZHI YUAN , GENQI XU
Email addresses of all the authors: ywzywz123@163.com ,gqxu@tju.edu.cn
Number of paper pages: 14
Abstract: In this paper, we analyze the spectra and stability of a system consisting of a working unit and repair unit, in which the working unit consists of one main unit and one standby unit, while the standby unit may deteriorate in its standby mode. Firstly, we formulate the problem into a suitable Banach space. And then we carry out a detailed spectral analysis of the system operator. Based on the spectral analysis and $C_0$-semigroup theory, we prove the existence of positive solution and finite expansion of the solution according to its eigenvectors. As a consequence we get that its dynamic solutions converges exponentially to the steady-state solution. Finally, we derive some reliability indices of the system.
Keywords: C_0-semigroup theory, dynamic solution, steady-state, exponential stability, availability.
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