Further Research Of The Transfer Line Consisting Of A Reliable Machine, An Unreliable Machine And A Storage Buer With Nite Capacity

This thesis consists of two chapters. The first chapter is divided into two sections. InSection 1, we introduce brie?y the history of the reliability theory. In Section 2, we introducesupplementary variable technique and then put forward the problems we are concerned in thispaper. Chapter 2 consists of two sections. In Section 1, firstly we present the mathematicalmodel of the transfer line consisting of a reliable machine, an unreliable machine and a storagebu?er with finite capacity, next we convert the model into an abstract Cauchy problem byintroducing state space, operators and their domains, lastly we introduce the main resultsabout this system obtained by other researchers. In Section 2, we study properties of theC0?semigroup generated by the operator corresponding to this model and prove that theC0?semigroup is a quasi-compact operator, thus we obtain that it converges exponentially toa project operator. For a special case, we deduce asymptotic property of the time-dependentsolution of this model.