Further Research Of The Cold Standby Parallel System Consisting Of Two Repairable Units

This thesis is divided into two chapters, the first chapter is split into two sections. In Section 1, we introduce creation, development and current research situation of reliability theory. In Section 2, we firstly introduce creation and thought of supplementary variable technique, then put forward the problem that we will study in this thesis. The second chapter is divided into two sections. In Section 1, firstly we introduce the mathematical model of a cold stanby parallel system consisting of two repairable units with two states, then we convert the model into an abstract Cauchy problem by introducing state space, operators and their domains. In Section 2, we discuss asymptotic property of the solution. First we will prove the C₀-semigroup generated by the operator corresponding to this model is a quasi-compact operator under the assumption 0<μ≤μ(x)≤μ<∞, then by combining the result with other's results we will deduce that the time-dependent solution of the system is exponentially stable. Last we will discuss point spectrum and residual spectrum of this operator whenμ(x) =μ, thus we give the structure of the solution of the model.