Reliability Analysis Of A Repairable Model

Three component series parallel system system is a kind of special repairable system,which has a wide range of applications in production practice and is an important research object of reliability theory and reliability mathematics.This kind of system belongs to the category of complex system.It must be based on the complex system ”according to the needs of system overall coordination,realize the combination of qualitative analysis and quantitative analysis,Based on the general principle of ”combination of theoretical proof and numerical calculation”,the reliability of the system is studied.In this paper,the mathematical model of a three component series parallel repairable system and its reliability are established and studied by means of functional analysis,stochastic process and semigroup theory of linear operators.The main contents are as follows:Chapter 1 is the introduction,which mainly introduces the research background and research status of repairable system,and gives the relevant knowledge used in the research of repairable system model;In Chapter 2,the mathematical model of the repairable system is established by using stochastic process theory and additive variable method,and the abstract Cauchy problem is obtained by using functional analysis method to transform the mathematical model;In Chapter 3,the semigroup characteristics of the main operator of the system are studied by using the semigroup theory of linear operators,The well posedness of the system solution is obtained;In Chapter 4,based on Chapter 3,the spectral distribution of the system operator is discussed by using the theory of functional analysis,and the asymptotic stability of the reliability system model is analyzed;In Chapter 5,the reliability of the system is studied by numerical calculation.On the premise of assuming the system failure rate and repair rate as constant,the reliability indexes such as transient reliability and steady reliability of the system are obtained,and the quantitative analysis of the repairable system model is realized;Chapter 6 is the summary and research prospect of the whole paper.