Other Eigenvalues Of The System Consisting Of A Reliable Machine, An Unreliable Machine And A Storage Buffer With Infinite Capacity

This thesis consists of two chapters. The first chapter is divided into two sections. In the first section, we introduce briefly the history of the reliability theory. In Section 2, we introduce supplementary variable technique and then put forward the problems we are concerned in this paper. The second chapter consists of two sections. In Section 1, firstly we present the mathematical model of the system consisting of a reliable machine, an unreliable machine and a storage buffer with infinite capacity, next we convert the model into an abstract Cauchy problem by introducing state space, operators and their domains, lastly we introduce the main results obtained by other researchers. In Section 2, we study eigenvalue of the operator corresponding to the model in left half complex plane, and obtain that (2(?)-λη1-μη2)θare eigenvalues of the operator with geometric multiplicity one for allθ∈(0,1).