Analytic Expression Of Complex System Reliability And Statistical Inference Of Some Characteristics

A complex system consists of several subsystems in certain way which is usually described by minimal paths or minimal cutsets and each subsystem's reliability immediately influences the system's. Therefore, the study on the reliability of complex systems has both theoretical significance and potential of application. In this thesis, we consider the complex system which is described by minimal paths or minimal cutsets, under the condition that subsystems are independent on each other. The main results are as follows:Firstly, the special operations of vectors and matrices are defined by using the minimal path matrix and minimal cutset matrix of systems. Through these special operations, the analytic expressions of the reliability functions of two-state complex systems are improved. Above analytic expressions are effective tools for the statistical inference of system reliability. The algorithm itself makes it easy to calculate the system reliability. Once the system's minimal path matrix or minimal cutset matrix and every subsystem reliability are inputted, the system reliability can be obtained directly by the computer programs.Secondly, the multi-state network system consisting of a source node, a sink node, and some independent components are studyed. For such systems, the analytic expressions and algorithm implementation for reliability of multi-state network systems based on all d-minimal path vectors are given. Once the network's d-minimal path vectors and state probability are inputed, the relability of network can be obtained directly by the computer programs.Thirdly, for two-state systems, the subsystem reliability impacting on the system reliability is considered. The properties of MRI (marginal reliability importance) estimations of subsystems are studied, the unbiasedness of above estimations are confirmed and the variance of them are given. Moreover, we prove that the difference of MRI estimations of subsystems is unbiased.Finally, the hypothesis testing problem of system reliability design is investigated, a testing method based on empirical likelihood is shown and the asymptoptic normality are proved.