The Analysis Of The Stability And Reliability Of A Repairable, Standby, Human & Machine System

Reparable system is one of the most important systems discussed in the reliability theory, and also the primary subject studied in reliability mathematics. Many scholars have done a lot of work about the well-posedness and asymptotic stability of the system. In this paper, we prove the eigenvalue problem and reliability for this system in theory.In a more detailed description, we first show that the system operatorgenerates a positive C₀ semigroup in the state Banach space. We also provethat system has a steady-state nonnegative solution which is just the eigenvector of the system operator corresponding to eigenvalue 0, and 0 is the unique spectral point of the system on the imaginary axis. Further, we prove the reliability of the system under some restriction, that is , the instantaneous reliability is more than or equal to its stable reliability. At last, we also prove the existence of non zero eigenvalue and an eigenvalue corresponds to an eigenvector.