The Analysis Of Repairable System With Reserve Componet Is Easy To Damage

Repairable system is a main object in reliability mathematics and also an kind of system discussed in reliability theory, and the generalized Markov model through the supplementary variable method; on the basis, studying the system reliability indices by use Laplace or Laplace-Stieltjes transform, and then discussing the problem of reliability,the main tool is the theory of random process.This paper mainly researches the reliability analysis of a repairable system with reserve component is easy to damage under common-cause failure and has already damaged parts reserve warning devices.First,we receives system nonnegative solution exists and the only with use the theory of Volterra integral equation,and transformation into Banach space in the of abstract of Cauchy problem with the system equations,the system operator is dissi-pative operator in Banach space and it generates semigroup is compressed Co-semigroup,we theory proved that the system is not negative time dependent on the existence and unique-ness of solutions with semigroup;Second,through the spectral analysis of system operator and its generated semigroup get the simple eigenvalue of the system operator is0, and prove the semigroup is quasi-compactness and irreducibility, so we get asymptotic stability and exponential stability of the system; Again,through the construction step function get semi-discretization of system model,and utilize theory the Volterra integral equation and the theory of semigroup respectively discussed system solution of approximation of the prob-lem; Finally,we discussed the influence of early warning devices in the system,the numerical simulation on certain conditions warning system with the early warning system steady state availability of the relative error of tend to be0.