Repairable System Stability Analysis Of A Warm Standby With Priority

Repairable system is the discussion of important issues in the theory of reliability, it is also one of the main research object of reliability mathematics.In this paper, by using the theory of semigroups, with priority retains heat reserve components was studied and the stability of the series repairable system. To the actual generation, life has the vital significance.In this paper,we study the stochastic behaviour of a complex system consisting of two subsystem A and B connected in series.Subsystem A has two unit arranged in standby redundancy,a main unit and a standby unit,whereas subsystem B consists of one unit only.Assumed that the failure rate of the standby unite changes when it is put into operation.Also his system is unrepairable.Here we assume that there and self life failure for all units.When the main unit in subsystem A fails,the standby unit takes its work immediately.Failure of subsystem A or B brings the system to complete break down state.The entire system can also due to human failure or hardware failure.This system model is a "first come-first served"discipline. In this system,repair is performed for the failed unit whenever the service facility is free. If the service facility is occupied and a unit fails,it must wait for its turn until the service facility becomes free.A subsystem in this model unit has priority, that subsystem A component failure in Advanced Placement, subsystem B in parts need to wait for repairs after it repaired.In this paper, we assume that all parts of the system after the repair can be such as no wear, parts of the system running time and storage time are subject to the index segment, failure time and repair time are subject to general distribution。The concrete can be divided into 14 kinds of state. First of all, in this article, through a number of assumptions and supplementary variable method is used to establish the mathematical model, and then selected the appropriate state space, the partial differential equation into abstract Cauchy problem; Again by the upper and lower bounds of the spectrum of the system’s host operator is obtained by the valuation of tail show that generated by the system’s host operator semigroup of growth and the growth of the system’s host operator boundary are equal, and continue to prove the existence and uniqueness of time-dependent solution of the system. Finally using the operator perturbation theory steady-state solution of this system and the exponential stability of the system.