Another Eigenvalue Of The System Consisting Of A Reliable Machine, An Unreliable Machine And A Storage Buffer

This thesis consists of two chapters. The first chapter is divided into twosections. In the first section, we introduce briefly the history of the relia-bility theory. In the second section, we introduce supplementary variabletechnique and then put forward the problems we are concerned in this pa-per. The second chapter consists of two sections. In Section 1, firstly wepresent the mathematical model of the system consisting of a reliable ma-chine, an unreliable machine and a storage buffer with infinite many work-pieces, next we convert the model into an abstract Cauchy problem byintroducing state space, operators and their domains, lastly we introduce themain results obtained by predecessors. In Section 2, we study eigenvalueof the operator corresponding to the model in left half complex plane, andobtain thatλη₁μη₂^1/2-λη₁-μη₂ is an eigenvalue of the operator withgeometric multiplicity one.