Research On Three Types Of Signature And Its Application

Signature theory is the intersection of structural reliability and stochastic reliability.The research of signature mostly focuses on the exploration of its theoretical properties and its application in practical problems.This paper proposes two new signature from the two backgrounds of system and component correlation analysis and system complexity;At the same time,from the perspective of statistical reliability,a non-parametric statistical estimation method is proposed for survival signature,and based on this estimation,the important problem of component lifetime distribution estimation is studied.Based on system signature,develop and propose component signature.According to distribution of conditional random variable,it is pointed that system signature reflects the dependence structure between overall component group and system,but fails to reflect that between a certain single component and system.In response to this problem,this article defines the component signature from the perspective of component lifetimes themselves.And based on the proposed signature,establish the corresponding conditional distribution from both continuous and discrete cases to present the dependence structure between a certain single component and system.Finally,component signature is used to compare and estimate MTTF.For survival signature,propose a non-parametric statistical estimation method.In a coherent system consisting of independent homogeneous components,from the perspective of the number of failed components in the system when the system fails,an estimation method is proposed in the case where the system structure is completely unknown,and then from the perspective of asymptotic analysis,the statistical characteristics of the estimator are analyzed.In the coherent system consisting of multiple types of components,the estimation method is further extended.An estimation method based on the number of failed components and a computation algorithm based on the failed cases are established,and the two methods are compared.Finally,based on the proposed estimator of the survival signature,the problem of inversely estimating the component lifetime distribution through the estimation of the system lifetime distribution is solved,and its superiority compared with traditional methods is proved from the perspective of asymptotic variance.Then simulation analysis is performed.For system complexity,propose parallel signature.In view of the fact that there is no common measure of system complexity,from the perspective of the parallel system structure,parallel signature is proposed.Based on this signature,the complexity of different systems can be compared.Then in the coherent system consisting of heterogeneous components,complexity comparison based on parallel signature fails.Thus PSTI and SPSTI graphical analysis techniques are proposed to compare the complexity of different systems.Then simulation analysis is performed.