Further Research Of The K/N: G Redundant System With Repair And Multiple Critical And Non-critical Errors

This thesis consists of two chapters. The first chapter is divided into two sections. In section 1. 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. Chapter 2 consists of two sections. In Section 1, firstly we present the mathematical model of the k-out-of-N:G redundant system with repair and multiple critical and non-critical errors, next we convert the model into an abstract Cauchy problem by introducing state space, operators and their domains, lastly we introduce the main results about this system obtained by other researchers. In Section 2, we study properties of the C₀ - semigroup generated by the operator corresponding to this model, we prove that the C₀ - semigroup is a quasi-compact operator, thus we obtain that it converges exponentially to a project operator. For a special case, we deduce asymptotic property of the time-dependent solution of the system.