The System Analysis Of Reparable Systems Model

Repairable system is the main research object of reliability theory and reliability mathematics. Because of the system analysis of repairable system model involving all kinds of links and factors of the established mathematical model, including the com-prehensive utilization of the theories and methods of many disciplines such as systems engineering, reliability theory, the theory of stochastic process, the theory of differen-tial equation, the linear operator semigroup theory, etc., touching upon the application of computer technology such as numerical calculation, numerical simulation and so on, therefore, in a sense, the system analysis process of repairable system model is a systems engineering, must be based on the needs of overall coordination, to combine them or-ganically and study them separately. For this reason, based on the needs of the actual research background and the cognitions of the meta synthesis approach from qualitative to quantitative, and the thinking of the current researches and existent problems of re-pairable system model, proposed the application of the meta synthesis approach from qualitative to quantitative, developed the system analysis research topic of repairable system model.Around the above research subject, this paper firstly analyzed the current researches and existent problems of repairable system model, introduced the related concepts and theories of repairable system, and on this basis, the system analysis method of repairable system model which uses meta synthesis was put forward; Secondly, introduced the re-lated contents of a special kind of linear operator semigroup-C0 semigroup, these contents play an important role on the discussions of the well-posedness and asymptotic property of the repairable system model, are the mathematical tools and theoretical foundations of studying the repairable system model; Afterwards, by the theory of stochastic process and supplemented variables, a parallel repairable system with two non-identical unit was established, and converted the system model into convolution Volterra integral equation and abstract Cauchy problem in Banach space according to the needs of system anal-ysis. Be aimed at the repairable system model, using the theory of Volterra integral equation and C0 semigroup, the existence and uniqueness of the nonnegative solution of the system, the well-posedness and asymptotic property of the solution of the system were discussed, and proved the exponential asymptotic property of the solution of the system under some additional conditions; In the meantime, the problems of reliability, controllability, optimal control and the semi-discretization of the system model by using the theory of differential equation and Banach space were studied, and according to the methods of numerical calculation and the numerical simulation, some conclusions drawn from this thesis have been proved.This dissertation is intended to study the actual research of a parallel repairable system with two non-identical unit, try to find out a effective way of the system analysis for the repairable system model, and so as to provide reference for realizing the systemic, overall, scientific research on the repairable system especially the complex repairable system.The meaning of this dissertation shows that it can provide a new method for the research and the application of the repairable system model, it would not only benefits to enrich the repairable system theory, but also to promote the application of reliability theory and reliability mathematics, and to provide the scientific evidence and technical support for the production and management decision-making on military, aviation, space-flight, computer technology.The major contributions and innovations of this dissertation are as follows:(1) Utilizing the meta synthesis approach from qualitative to quantitative, so as to analyze a parallel repairable system model with two non-indentical units systematically, to wish can be rich and perfect the theory and method of repairable system, and in order to provide implementation for realizing the systemic, overall, scientific research on the repairable system.(2) Using the theory of functional analysis, to study deeply about linear operator with dissipative characteristics, in order to get new generation theorems constantly, and provide theoretical basis for studying the repairable system.(3) By the method of numerical calculation, so as to carry on numerical simulation for repairable system model, in order to obtain the quantity index of reliability such as the reliability, availability and maintainability of system dynamics and so on, and to provide the evidence for further developing the reliability analysis.