Further Research On The System Which Consists Of A Repairable,Standby Human And Machine

This thesis consists of two chapters.The first chapter is divided into two sections.Section 1 introduces briefly the history of the reliability theory.In Section 2,we introduce the supplementary variable technique and then put forward the problem we are concerned in this thesis.Chapter 2 consists of two sections.In Section 1,firstly we present the mathematical model of the system consisting of repairable,standby,human&machine,next we convert the model into an abstract Cauchy problem by introducing a state space,operators and their domains,lastly we introduce the main results obtained by other researchers.In Section 2,firstly we determine the expression of the resolvent of the operator,next we show that 0 is a pole of the operator of order one,thirdly by combining these results with the residue theorem we give the expression of the projection operator appearing during research of this model.Finally,we deduce that the time-dependent solution of this model converges exponentially to its steady-state solution.