Research On The Dynamic Signature And Remaining Life Of Polymorphic Interconnected Systems

System signature,represented by a probability vector which relies on the system’s structure,is a powerful tool for reliability analysis.Thus,reliability of the system can be well-modeled by signature but not necessary to know lifetime distribution of the components.In addition,it is easy to measure the performance of components’failure and system’s lifetime by calculating the signature.Recently,owing to clarity in definition and simplicity in application,system signature has attracted great attention in academia.As a result,there are booming researches on reliability modeling on a basis of signature and lifetime comparisons between different binary systems,and the signature theory tends to be mature.On the other hand,studies on signature for multistate systems’ reliability analysis are far more enough.In fact,the potential value of signature in multistate analysis is not fully recognized.In many engineering practices,however,systems and components are not simply presented as success or failure but a number of intermediate states between these poles.If they got only two states,it will cause serious deviation from the real situation.Therefore,how to come up with an proper-extended signature and apply it to the reliability analysis of multi-state systems will be the core of this research.The research concentrated on two types of coherent systems:The first type of systems consists of n binary components,whose failures cause a decline on system’s performance in a cumulative way.The performance level of the system depends on the number of available components-the greater the number of available components,the higher the performance level of the system.The second one is composed of multi-state components.The performance of the system deteriorates as the components that make up the system get worse(for example,component fatigue)over time,or due to changes in the external environment.For the first type of system,the definition and scope of the traditional signature should first extend to a multi-dimensional situation,whose aim is to apply it directly to multistate systems.Thanks to a framework of multi--state system theory,the joint survival function is obtained.After that,we further explore dynamic signature of the system at a certain moment.In other words,dynamic signature is a conditional failure probability vector,and the conditional events are as follows:the multi-state system is still working at time t,and the system is found to be in state l(t)or above as well as q(t)th failure.On this basis,the algorithm for dynamic signature and the solution the residual lifetime of the system are eventually obtained.A numerical example is given to verify the validity of the method.For the second type of system,since the lifetimes of the same component in different state levels are not independent,we have to start with the survival signature.Survival signature is an extension of system signature,which is suitable for analyzing systems consisting of multiple types of components.The multistate components are regarded as two-state components in different state levels.Similar to Samaniego’s signature method,survival signature of the system in j th level and its algorithm are derived as well as the expressions of survival function in each level.Moreover,the concept of survival signature inversely defines the m order signature,and the corresponding calculation formula is given.Through the m order signature,it is easy to present the representation for lifetime distribution of the multistate system.Finally,the dynamic signature of the system based on conditional events is further studied according to the same way as the first type.The dynamic signature of the second type of system and the representation of its residual lifetime are obtained respectively.The given numerical example is a multistate consecutive-k-out-of-n system,and the computations verify the feasibility of this method.