Reliability Analysis Of Repairable System With Reboot Delay

After a repairable system has stopped due to a failure,it usually takes some time to recover or restart,this is called a reboot delay.A reliability model with reboot delay can more realistically describe engineering systems.Therefore,this model has gradually become a hotspot issue in the field of reliability research.This paper studies the reliability of complex repairable system with reboot delay established by using supplementary variable method and Markov process.This paper first introduces the mathematical model of a complex repairable system composed of two subsystems R and T in series.By selecting a suitable state space,the model is transformed into an abstract Cauchy problem in Banach space.Secondly,the existence and uniqueness of dynamic solution of the system are proved by using the resolvent positive operator and C0 semigroup theory.Then,the exponential stability of the system is obtained by analyzing the spectral distribution of the system operator and using the resolvent positive operator and cofinal theory.Finally,the optimal control element of the system is obtained by using the index functional as a criterion to measure the controllability of the system and using the minimization sequence method.