The Study Of Estimation Of Reliability For Complex System And Subsystems' MRI With Interval Censored Date

A complex system consists of several subsystems in certain way.Reliability of each subsystem immediately influences the system's reliability. In the actual applications, the data information directly from system is little, we usually can get relevant data information of subsystem, so the study of each subsystem's reliability by subsystem's obtained data information naturally is a problem with widespread attention. The forms of data information from subsystems usually are diverse. The system reliability statistical inferences are studied usually under the condition which subsystem distribution is known common type, or life data is completely known. Based on the complex systems discribed by minimum path or minimum cutset, life distribution of subsystem is general and life data from its system is incomplete. At present, this assumption precondition of research is little.Interval censored data is not completely a form of data. Therefore based on the interval censored data,statistical inference of the characteristic of the system's reliability are both the important theoretical significance and widespread application value. Based on the minimum paths of independent subsystems and general distributions of subsystem life, the reliability of complex systems is studied.The main research results are reflected in the following respects:Firstly, the complex system S ,which is described by the minimal path, has m independent subsystems which are S1 , S 2, L , Sm.Minimum path matrix is A .Each subsystem data is interval censored data. Through estimation of distribution function by interval censored data and the reliability function of complex system reliability, the estimation of complex system reliability based on interval censored data is given. Secondly, based on the complex system which is described by the minimal paths and whose subsystem's life data is interval censored data, the asymptotic distribution of reliability estimation is given.This provides a approximation method for solving the problems, for example the confidence lower limit of the system reliability and the hypothesis testings and so on.In this paper, it is only applied to the confidence lower limit of system reliability.Finally, for complex system whose subsystems life data is interval censored data, considering the problem of subsystem importance estimation, this paper presents asymptotic distribution of estimator for the Marginal Reliability Importance.