Complex System Reliability

With the development of science and technology, there have been somelarge-scale complex systems in recent years. These systems are closely related to ourlife. If these systems faulted, this would threaten the safety of our production and life.Therefore, it is necessary to study these system’s reliabilities. In addition, reliabilityanalysis requires a large number of accurate statistical data, however, in the practicalengineering, the collected data are often insufficient and imprecise due to manyfactors, and the system reliability can be influenced by the number of failedcomponents in system. So we need introducing fuzzy reliability theory to study thecomplex system reliability. Thereby, how to do the Reliability assessment for thecomplex system under traditional and fuzzy environments is essential and significant.We study the repairable combined m-consecutive-k-out-of-n: F and Consecutivekc-out-of-n: F System, based on the working time of each component is exponentiallydistributed. Firstly, the generalized transition probabilities between different states areobtained by using combinatorial mathematics and stochastic process theory. Thus, wecan obtain the generalized transition rate matrix. Further, we obtain the system’sreliability indexes by using the general method of solving the reliability of this classof system. Finally, a numerical example is given to illustrate the feasibility of thealgorithm.In order to discuss the reliability of the complex system, based on the workingtime of each component is not exponentially distributed, by using the distributiontheory for runs and studying the irreparable combined m-consecutive-k-out-of-n: Fand Consecutivek c-out-of-n: F System, the calculating approaches are obtained forthe reliabilities of the systems whose components are independent each other orMarkov dependent. Especially, the research approach for the reliability of the system,which components are Markov dependent, can be applied in more complex systems.When the system is functioning, its reliability may be influenced by the numberof the failed components. So the system fuzzy reliability theory is introduced to studythe repairable combined f-out-of-n: F and consecutive k-out-of-n: F system. We obtain the method of calculating the reliability of the system by defining the fuzzystates. The method considers not only the probability of the working states but alsothe influence of the number of failed components on the system.