| Reliability studies as an important area of research, is being more and more attention. Reliability Analysis of technological development is bound to greatly affect the reliability of system design and manufacturing. This is especially important in the country. Especially now that the development of an international trend, the domestic product to enter the international market to compete with foreign products, we must improve the performance and reliability of the product itself.Repairable system is one of the main object of reliability mathematics. The so-called repairable system, refers to the system consisted of a number of parts and one or more repair facilities(repairman). When the system components can occurred malfunction or deterioration, the repair facilities is going to repair through a variety of maintenance means, after repair a class of systems is as new as. With the intensive study, the stability of a reparable system is paid more and more attentions. In this context, the mathematical model of series-parallel repairable system with three unites with two types of failure state was established and its exponential stability by the new method was studied in this dissertation.Firstly, by using the supplementary variables method, the differential and integral equations was got. Secondly, combining the system equations and the boundary conditions, the state equations were transformed into the abstract Cauchy problem on the appropriate state space. The existence and uniqueness of dynamic solutions of the system was proved by using the semi-group theory. Thirdly, the spectrum distraction of the system operator was analyzed. Zero is a simple eigenvalue of this system operator and is also a unique spectral point on the imaginary axis was showed. The asymptotic stability of the system was then derived. Finally, by proving the quasi-compactness and irreducibility of the semi-group, the exponential stability of the system was given. |
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