The Reliability Research Of The1-Unit Repairable System With An Identical Warm Standby

We investigate the repairable system which is an1-unit system supported by an identical warm standby.chapter1, The background, significance of the theory, research ongoings at Home and Abroad, existed problems, main contents and methods in this dissertation are briefly introduced.chapter2, The mathmatics model of the repairable system which is an1-unit system supported by an identical warm standby is introduced.chapter3.Firstly, the proof of existence and uniqueness of nonnegative solution of the system is given, by converting model equations into Volterra equation in Banach space. Secondly, using Co semigroup theory, we first prove the system operator is a densely defined resolvent positive operator. Then, we obtain the adjoint operator of the system operator and its domain. Furthermore, we prove that0is the growth bound of the system operator.and, we show that0is also the upper spectral bound of the system operator using the concept of cofinal and relative theory.chapter4, The asymptotic stability of the system is discussed by analyzing the spectra distribution of the system operator and its dual operator. The system is asymptotic stability because the spectral points of the system operator and its dual all lie in the open left half plane and there is on spectrum on the imaginary axis except0.chapter5, The mathmatics model of the repairable system with warm standby, two same parts with warming function is introduced.By choosing state space and defining operator of system,we transfer mondel into an abstract Cauchy problem.we prove property of system solution by operator theory.chapter6, we consider the steady-state availability of a system with warming function and a system without warming function on the point of eigenfunction view.Then we prove that as hazard rate a approaches to infinity, steady-state availability of a system with warming function approaches to a system without warming function.