Reliability Modeling And Evaluating On Complex Redundancy Systems

The redundancy system is a significant type of mathematical models in system reliability field.The capacity of a system for resisting the risk of failure can be enhanced and the loss of capital and manpower can be decreased,if designed with redundancy.It is the development of system function that leads the reliability modeling for redundancy system subjected to multiple factors.In this thesis,based on two types of redundancy systems,i.e.,k-out-of-n and consecutive-k-out-of-n,the factors like multi-failure criterion,components spatial distribution,operating environment and component dependency are involved into consideration while modeling for system reliability.New reliability models are presented,by deriving the equation for calculating the reliability indexes and proposing the reliability evaluating methods.The research works of this thesis are including:First,based on consecutive-k-out-of-n,two reliability criterion,i.e.,multiple consecutive-₁k and single consecutive-k₂,where k₁?k₂,that lead the system fail or work are considered.By introducing the parameter l to represent the number of overlapped runs between two adjacent“consecutive-k runs”and the parameter m to represent the number of the“l-overlapped consecutive-k runs”,the model of“m-consecutive-k,l-out-of-n”is proposed.The new model is a general model of consecutive-k-out-of-n.By adjusting m and l,the new model can be translated into consecutive-k-out-of-n or m-consecutive-k-out-of-n models.The duality of linear?circular?“m-consecutive-k,l-out-of-n”model is demonstrated and the reliability evaluation method of“m-consecutive-k,l-out-of-n”model is obtained.Second,based on consecutive-k-out-of-n,by considering the components spatial distribution,the models of“consecutive-_rk-out-of-_rn:F with linear zigzag structure and circular polygon structure”are presented.In this new model,the components are non-uniformly distributed in several subareas.Two adjacent subareas share a common component which is called the shared component.The reliability equations of the consecutive-k-out-of-n given the states of the first and?or?last component are obtained,so that the rules for enumerating and calculating the reliability of the new models are established.The equation for computing the Birnbaum importance and joint reliability importance of the shared components are derived.Third,based on k-out-of-n,involving the influence on reliability criterion caused by cyclic alternating environments,the model of“dynamic k-out-of-n:F operating under cyclic alternating environments”is presented.For this new reliably model,the operating environments are appeared sequentially and each of them is assumed to follow a known probability distribution.The state of the components is switched by the time epoch of environment shift.If a component cannot switch into the corresponding state,it is regarded as failed.If the number of failed components violates the reliability criterion,while operating under a certain environment,the system is considered to be down.The approximation method for computing the reliability is provided for the new model.Forth,based on k-out-of-n,referring in some application,the system can operate only when the dependent components are all working,the model of“weighted k-out-of-n:G with component dependency”is proposed.By employing the finite Markov chain imbedding approach,the equations of some reliability indexes are obtained.Through specifying the component dependency relationship,the weight of subsystems,and the positions of the components,the new model can be translated as the models of“k-out-of-n:G”,“weighted k-out-of-n:G”,“k-out-of-n pairs:G”and“k-out-of-n pairs:G balanced”.The thesis has important significance in theoretical and practical in reliability field.The research works are brought about by observing the features of the redundancy systems in real application,which leads the invention of the new reliability models,with providing the method for evaluating reliability and the equation to computing the reliability indexes.The consequences of this thesis enrich the research on reliability modeling on redundancy systems and can be applied for decision making.