The Study On Reliability Models In Repairable Redundant System

Since 1950s, theory of reliability and its applications have developed rapidly. Currently, it has infiltrated into the basic sciences, technological sciences, applied sciences and management sciences, and it has been more and more attached importance to. Reliability analysis of repairable systems is a greatly important branch of the theory of reliability.Repairable systems are those that get repaired when they fail. This is done by repairing or replacing the failed components in the system. In order to enhance the reliability of some repairable systems, redundant systems are commonly considered. At present, reliability models in repairable redundant system have been studied by many researchers, and at the same time, some related reliability indexes are derived. These works are not only advantageous for further reliability theory and application study but also practical significance. However, with the fast development of science and technology, all kinds of engineering systems are becoming more and more complicated, for instance, assembly lines, communication equipment, nuclear power plant, air traffic control system and so on. These systems are massively expensive to build, once they fail to operate as designed, the failure influence not only the enormous loss of national economy but also safety and stabilization of community, economic development of a country. So the study of reliability models in repairable redundant system need to be discussed deeply. The dissertation develops as follows:In the first chapter, introduces the significance, present condition of reliability models in repairable redundant system, then the author summarizes the concepts of reliability indexes and mathematical theory for repairable models, and fuzzy reliability analyzing the redundant system models.In the second chapter, parallel repairable redundant models with two components and parallel repairable redundant models with n components are discussed, some corresponding reliability indexes are obtained, and the fuzzy reliability indices for parallel redundant models are developed by using the principles and methods of fuzzy mathematics.In the third chapter, on the base of the existing research harvest, k-out-of-n: F repairable redundant models with one repairman and k-out-of-n:G repairable redundant models with m repairmen are studied, some important performance indexes are developed, and the fuzzy reliability indices for 2-out-of-4: F and k-out-of-n:F redundant models are determined by using the theory of fuzzy reliability.In the fourth chapter, on the basis of Markov theory and Markov renewal theory, the author presents the main indexes of standby repairable redundant models with two components and standby repairable redundant models with n units, and supplies the fuzzy reliability analysis for standby redundant models with n components, fuzzy reliability, fuzzy failure rate, and fuzzy mean time are worked out.In the fifth chapter, consecutive-k-out-of-n: F (G) repairable redundant models, which are more general models in practice, are investigated. Based on the general theory of reliability mathematics and some valuable conclusions of the models, for example, generalized transition probability and key component, several complex consecutive-k-out-of-n: F redundant models are analyzed in detail, and the algorithm of fuzzy reliability indexes for linear or circular consecutive-2-out-of-3: G redundant models are given by using the theory of fuzzy reliability.Conclusions, summarizes the results derived in this thesis, and some suggestions for further study are proposed.