Generalizatiom Of Several Importance Measures And Statistical Analysis Of Correlation Failure

Importance measures are the theoretical basis of the optimization of system performance, and play an important role in reliability engineering. Now the definitions of importance measures are based on the reliability, the structure function and the life distribution.Birnbaum importance quantifies the importance of components by the reliability. In real life the diversity of components, complex system, make it difficult to estimate components or systems reliability, thus affect the evaluation of Birnbaum importance. For practical needs, based on the observable output performance the models of importance measures are established. According to the influence of the unit changes of component state on systems availability, we can estimate the components importance. In multi state system, the initial state of the components is different, and the importance of components will be slightly different. In order to avoid the influence of state of components, the Birnbaum performance importance is established by taking average. In the two state system, we can not take average, because the degeneration of components only is working to failing. In the numerical analysis, the method of Lz-transform is adopted.Hazard rate is an important index to describe the reliability of components, but it is seldom used to study importance measures. In the paper the concept of conditional hazard rate is introduced and the related properties are deduced, and the model of hazard rate importance is established. The importance is established by the effects of components on hazard rate of the system. Further, according to the states of the components, the hazard rate importance is divided into the improvement potential hazard rate importance and risk achievement hazard rate importance; on the other hand, in order to solve the redundancy allocation problem, according to the parallel redundancy mode, the model of redundancy hazard rate importance is established. The best position of redundant allocation is evaluated based on hazard rate. In the numerical analysis, the exponential distribution and Weibull distribution are discussed.Most of the researches of importance measure are based on the assumption that components are independent. This paper studies reliability importance measures and structure importance measures of components in the systems that components are dependent. It uses Copula function fitting dependent structure among multiple components, and from the description of important measures of the various types, through a series of mathematical treatment, builds corresponding importance measures evaluation model of components involving failure correlation. In complex and practical k/n(G) system, it uses equivalent mapping between reliability calculation and representation of structure function to model for three types of importance measures evaluation involving failure correlation.