Study Of Reliability For Complex System

Some independent subsystems constitute a complex system in certain way.A familiar series system and parallel system are simple complex systems. Thenetwork system and coherent system are also complex systems. A complex systemis usually described by minimal paths or minimal cutsets. A problem of complexsystem reliability based on minimal paths or minimal cutsets is mainly researchedin this paper.Each subsystem's reliability immediately in?uences the system's. Therefore,the scholars from di?erent research fields have focused on such systems'reliabilityfor long, and the corresponding results are quite abundant.The research of thiskind of problem is important and valuable both in theory and in application. Acomplex system is usually described by minimal paths or minimal cutsets. In thispaper, the system reliability are researched under the conditions of supposing thatsubsystems are independent each other and minimal paths or minimal cutsets areknown. The central results are as follows:1.The system's minimal path matrix and minimal cutset matrix are intro-duced. The special operations of vectors and matrices are defined. Through thesespecial operations, the analytic expressions of complex system and multistate sys-tem reliability functions and each algorithm implementation are given. Analyticexpressions'acquisition provide an e?ective tool for the system reliability's statisti-cal inference. The algorithm itself makes it easy to compute the system reliability. Once input the system's minimal path matrix or minimal cutset matrix and ev-ery subsystem's reliability, the system's reliability can be obtained directly by thecomputer programs.2.Supposing that (a) subsystems are independent each other and the distribu-tion function of every life variable is unknown but the second moment is existent,(b) the life data on subsystems is known. Under the two conditions above, thesystem reliability estimator is given by using the obtained system reliability an-alytic expressions , its property is researched. It is proved that the estimator isunbiased. The estimate variance is given and the estimator's asymptotic normalityis proved. Simultaneously,The commonly three estimators are compared.3.The in?uence to the system reliability because of the change of the sub-systems is studied .In the research of the system reliability, we often suppose thesubsystem's data follows some kind of distribution, but if the hypothesis has cer-tain deviation, there should be in?uence on the system reliability's evaluation.There are much indices to evaluate the in?uence of the subsystem reliability tothe system's. The system's MRI(marginal reliability importance) is an objectiveand important index to describe this kind of in?uence. In this paper,the analyticexpressions and algorithm of the system's MRI are given. The statistical inferenceabout the MRI is also considered. The estimator of the system's MRI is given andits property is studied. its unbias and asymptoptic normality are proved. Theestimation of the di?erence between two subsystems's MRI is studied.4.Some applications of theoretical results in this paper are given. For in- stance,the simulation of system reliability and its conference limits, the design ofsystem reliability, the comparison between two subsystems's MRI.The research from item two to item four is completed based on item one.