Research On Dynamic Solutions Of Two Types Of Degenerate Repairable Systems

Deteriorating repairable system is a very important and common system,which has wide applications in machinery,chemical industry and other fields.This thesis uses the theory and method of functional analysis to dynamically analyze two typical deteriorating repairable system models in actual production,and study the dynamic solution of two types of deteriorating repairable system models.Model 1:A multi-state deteriorating system with minimal repairs and the replace-ment policy in general distribution,which is described by 2n+1 partial differential and integral equations with boundary conditions.By using functional analysis method,espe-cially linear operator's C₀-semigroup theory,we prove the well-posedness of the system and the existence of a unique positive dynamic solution.In addition,by analyzing the spectral properties of the system operator and conjugate operator,we prove the dynamic solution of the system converges strongly to its steady-state solution.Model 2:A deteriorating system with single vacation of a repairman,which is de-scribed by infinite partial differential and integral equations with boundary conditions.By using linear operator's C₀-semigroup theory,we prove the well-posedness of the sys-tem and the existence of a unique positive dynamic solution.And then,we prove that all points on the imaginary axis except zero belong to the resolvent set of the system oper-ator,further prove that zero is not an eigenvalue of the system operator,which implies that the steady-state solution of the system does not exist.