Study Of The Dynamic Solution Of A Parallel-series Repairable Deteriorating System Consisting Of Three Units With Multiple Delay Vacations Of Repairmen

Parallel-series repairable system is widely used in many field such as electricity and mechanical automation.In this thesis,we do dynamic analysis for the parallel-series repairable deteriorating system consisting of two repairmen and three units with multiple delay vacations of the repairmen.The system can be described by infinitely many partial differential equations.Firstly,we convert the system into an abstract Cauchy problem in a suitable Banach space,and we give the explicit form of the Dirichlet operator and characteristic equations,which correspond to the system.Then by using Phillips theory we prove that the corresponding operator of the system generates a positive contraction C0-semigroup.Finally by using C0-semigroup theory we prove that the system has a unique positive time-dependent solution.