Reliability Analysis Of Several Classes Of Multi-state Complex Systems

Reliability analysis of multi-state complex systems is one of the mainstream research directions in the field of reliability engineering and system safety applications.With the large-scale application of multi-state complex systems in computer networks,mechanical engineering,power grid systems,manned spacecraft,transportation,civil engineering,and fault detection,a large number of reliability-related problems have appeared,and more and more problems have been encountered,which have received extensive attention from more and more system engineers and scientific research scholars.Multi-state complex systems have the characteristic-s of multi-state,multi-phase,multi-function,high reliability,small sample size,long lifetime,complex dependence and random uncertainty,etc.The reliability models of these complex systems are described and analyzed based on classical reliability theory that has become more and more difficult.The models and functions of these complex systems are simplified based on the classical reliability theory,and the reliability of the simplified system is used to approx-imate the reliability of the complex system,and relatively large errors or even wrong results may occur by using this method.Therefore,according to the characteristics of multi-state complex systems,one can utilize the reliability mathematics,reliability engineering,reliabili-ty management and other related research methods to study the reliability design of modern complex systems,experiments and analysis and other new methods and new technologies have important theoretical significance and practical application value.The purpose of this thesis is to study the reliability modeling and analysis of three class-es of multi-state complex systems with the background of electric power system,computer network and communication networks.The first class is the reliability modelling and op-timization modeling methods for dynamic systems under several different system structures based on performance sharing mechanism;The second class is to discuss the reliability mod-elling and evaluation for dynamic phased-mission systems exposed to Poisson Shock;The third category is to consider the reliability of a class of dynamic network system subject to probabilistic propagation failures and failure isolation effects.In order to solve the reliability problems of the above-mentioned systems,this thesis comprehensively utilizes the universal generating function,the binary decision diagram technique,the modular method to analyze the working principles of the three different multi-state system structure models under the per-formance sharing mechanism,the reliability evaluation of complex systems for phased-mission system under Poisson shock,and the reliability modeling of complex network systems with the probability propagation failure and isolation effects.In the introduction of Chapter 1,the gen-eration and related application background of the three classes of multi-state complex systems are introduced in detail,as well as recent research results and current research deficiencies and problems that need to be resolved.According to the different problems concerned the main content of this thesis is organized from the following five parts.In Chapter 2,the reliability analysis and related optimization problems are investigated for a multi-state complex system with performance sharing mechanism.The considered com-plex system is composed of m heterogeneous k/n(G)subsystems and a common bus.Each subsystem i contains n_idifferent components.The performance of each component and the demand of each subsystem are a random variable with finite states.The reason for the failure of the subsystem i may be that its performance cannot meet its own demand,or the number of its normal working components is less than its own required minimum number of k_i.With the performance sharing mechanism,any subsystem in the system can share its remaining performance after meeting its own needs through the common bus to other subsystems with performance deficiency.After the performance sharing,the requirements of all subsystems can be met,and the entire system is reliable.Then,bivariate universal generating function algorithm is utilized to evaluate the reliability of the whole system,and an analytical example and a numerical case are utilized to verify the rationality and applicability of the model.Fi-nally,the structural optimization of a performance sharing system with limited transmission capacity is discussed.In Chapter 3,the reliability modelling analysis is investigated for a multi-state series complex system with performance sharing mechanism.The system consists of m heteroge-neous k/n(G)subsystems in series,each adjacent subsystem is connected by a performance transmission line,and each performance transmission line has transmission capacity limit.The difference between this model and the model in Chapter 2 lies in the way the subsystems are connected.In the previous model in Chapter 2,all subsystems are connected to the Common bus.The subsystems in this model are connected in series through the transmission lines.The surplus performance of the two adjacent subsystems in the system can be shared through the transmission line connected to them,and then the collected performance is further transmitted and shared through the next adjacent transmission line,until the performance sharing of the entire system is realized.Then,based on the constructed bivariate universal generating func-tion algorithm,the reliability of the entire system is evaluated.Finally,an analytical example and a numerical case verify the rationality of the model and the effectiveness of the proposed method.In Chapter 4,the reliability problem is investigated for a star structure multi-state com-plex system with performance sharing mechanism.The considered complex star structure system is composed of two categories of subsystems,The first category is the main system of the system which occupies the central location of the star structure,and the second catego-ry are reserve subsystems distributed at the terminal locations.Both the performance and the demand of each subsystem are random variables,and the transmission lines have limit-ed performance transmission capacities.The reserve subsystems are connected to the main subsystem in a point-to-point manner through intermediate transmission lines.The surplus performance of all the reserve subsystems can be transmitted to the main subsystem through the transmission lines between them,and then the excess performance of the main subsystem can be further transmitted to reserve subsystems experienced performance deficiency,too.The system is reliable if and only if the demands of the main subsystem and several reserve sub-systems are satisfied after performance redistribution.An algorithm based on the universal generating function technique is developed to calculate the reliability of the proposed system with performance sharing.An analytical and a numerical example are presented to illustrate the advantages and applications of the proposed method.In Chapter 5,the reliability problem is investigated for phased-mission system exposed to Poisson shocks.It is assumed that the components of system obey the non-exponential distribution and the shock obeys the homogeneous Poisson process,the semi-Markov process theory is applied to analyze the state probability of the subsystem,and the random process theory and the approximate integral calculation method are combined to obtain the failure distribution function of the electronic components under the random shock.In addition,the reliability evaluation of dynamic complex systems with phased-mission requirements is realized by using binary decision diagram technique and the modular method.Finally,a practical numerical case is used to verify the proposed model and method.In Chapter 6,the reliability problem is investigated for a network system subject to probabilistic propagation failure and failure isolation effect.Probabilistic propagation failure considered in this Chapter is the failure of some components in a system,which will cause other components to fail with certain probabilities.Failure isolation means that the failure of a trigger component will lead to its corresponding dependent components being isolated from the network system.Since the failure isolation effect is activated only when the failure of trigger components occurs before the occurrence of probabilistic propagation failure,there exists a competing failure in the time domain between the failure of a trigger component and the components with probabilistic propagation failure effect.Then,a combinatorial method based on binary decision diagram is proposed to analyze the reliability of the network systems subject to probabilistic propagation failure and failure isolation effects.At last,a numerical case is used to verify the universality and effectiveness of the proposed model and method,and the sensitivity analysis for the parameters of components and propagation failures is further studied.Finally,in the end of this thesis,we summarize the relevant work of the thesis,and point out several research issues and research directions that the author intends to continue in the future.