Study On The Dynamic Solution Of A Series-parallel Repairable System Consisting Of Three-unit With Multiple Vacations Of A Repairman

This thesis is divided into three chapters.Chapter 1 split into two sections.In Section1,we introduce the current research states and significance of repairable systems at home and abroad.In Section 2,We talk about research methods and main ideas.Chapter 2consists of four sections.In Section 1,we introduce the mathematical model of a kind of series-parallel repairable system consisting of three-unit with multiple vacations of a repairman.In Section 2,we convert the model into an Abstract Cauchy Problem in a Banach space.In Section 3,we give the explicit form of Dirichlet operator.In Section4,We prove that system operator generates positive constructive C₀-semigroups.Thus we prove existence of a unique positive dynamic solution of the system,by using C₀-semigroup theory of linear operators.Chapter 3 consists of two section.In Section 1,We study the spectrum of the system operator and write expression of resolvent system operator.In Section 2,we prove the irreducibility and the asymptotic behavior of the semigroup generated by system operator.Thus we obtain asymptotic stability of the dynamic solution of the system.