The Analysis Of The Stability And Reliablity Of Reparable System With Warm Standby

Reparable system is one of the most important systems discussed in the reliability theory and also the primary subject studied in reliability mathematics.This paper mainly investigates the stability and reliability of the reparable systems described by generalized Markov models,which are formulated by supplementary variable technique.It is significant for the reliability of the systems.Many scholars have done a lot of work about the well-posedness and stability of the systems.However,the problem of an eigenvalue of the systems and the relationship of the instantaneous reliability and the stable reliability are not be well proved.This paper presents a model of a two identical units parallel reparable system with warm standby.First,we show that there exists a unique nonnegative time-dependent solution of the model by using the Volterra operator equation.Besides,we get the conclusion an eigenvalue corresponds to an eigenvector and the existence of nonzero eigenvalue besides zero.At last,we prove the relationship of the instantaneous reliability and the stable reliability,we finish the proof of the reliability of the solution of the systems.