The Reliability Study On Some Warm Standby Repairable Systems

Reliability theory research has attracted a lot of scholars, there has been a largenumber of papers and research achievements about it ever since1830s. Howeverprevious researches basically are aimed at system consists of cold standby system,for the warm standby system especially the warm standby system attacked bypoisson shocks are extremely rare.By using the theory of Markov process theory, judging by the basis of theformer Scholars and their researches, three types of the warm standby system withstandby components and perfect switches are analyzed.The first system is the mixed standby system with two standby parts. Buildingthe model in order to make discussion easy, and a series of reasonable assumptionsare put forward based on the model, such as switch instantaneous, all variables areindependent to each other, parts are new after repairing. According to theassumptions of the system, all possible states are listed, then we get the transferprobability and the rate about its change matrix. Again, according to the Markovprocess theory, a series of equations are put forward. By using Laplace transformand inversing Laplace transform, the system reliability and some other reliabilityindices are calculated.The second system is three warm standby system with two standbycomponents. The same model is established as the first system, and a series ofassumptions about the model are put forward. The main difference is that theassumptions under the model from the first system is components in differentstandby states when they are normal.The third type system is a loop warm standby system with one warm standbycomponent, the system is more general. Here a new model different from twoupper model is established. But the basic assumptions remain unchanged.For the three types of systems, the three simple parts of the system is firstdiscussed and then expanded to the corresponding system attacked by poissonshocks. According to our hypothesis that three kinds of systems are Markov repairable system, and by using the Markov process theory, we can conclude theirtransition probability and its rate matrix. By using Laplace transform and inversingLaplace transform mathematical method, the reliabilities of the systems and somereliability indices are calculated, such as mean time to first failure. The example ofsystem steady-state fault and a simple simulation are given in every chapter.