The Reliability Analysis Of Two Types Of Systems With Warm Standby Components

Series system and k/n(G) system have a pivotal position in the reliability mathematic filed. In the real world, depending on the difference of the types of components and system construction, algorithms for reliability of Series System and k/n(G) system are quite different The most important task in this thesis is to study reliability of Series System with warm standby components and k/n(G) system based on the difference of failure rate of components working and standby.Firstly, considering Series repairable system consisted of three nonidentical components with one warm standby component. Three working components in system have repair priority, that is, when the system has standby component failure, failure is also working components, repair the union priority repair working components. When the working life distribution, repair time distribution and reserve life distribution of components are subject to different parameters of the exponential distribution, using the homogeneous Markov process, analyzing deduced specific analytical expressions of system availability, reliability and system mean time to first failure other reliability index.Secondly, researching the reliability of four to take three voting system consisted by two types of components and one warm standby component. Four components have two I type components and two II type components, and one I type components for warm standby components. Life distribution, repair time distribution and storage life distribution of I type and II type components are exponential distribution with different parameters, to study the reliability of the system with Markov process. Analysis the state transition rules of the system, obtain a set of differential equations of distribution satisfied of the system. Using Laplace transform obtain the laplace transform expression of pull transform instantaneous availability of systems; using steady-state indicator method get the system stable availability; combining absorbing state applications, introducing the Laplace transform, getting the Laplace transform expression of system reliability. In addition, the use of the Laplace transform solve for system reliability in the absence of repair situations.Finally, two specific numerical examples in Chapter4used to validate the numerical solution of the model can be obtained by computing solution, using Matlab software programming, running out the availability and reliability of the system, and the average time of system failure. Using Matlab software draw an image of system reliability, and analysis the variation of the system reliability with time.