Research On Reliability Analysis And Optimization Based On The Multi-State System Theory

The method for reliability analysis and optimal design of large complex systems and important products is treated as a technology related to the national strategies. The technology has been included in the National Medium- and Long-Term Program for Science and Technology Development (2006—2020), and in the National High Technology Research and Development Program. The related theories and technologies need to be researched.When the reliability of complex systems is analyzed and optimized by the traditional reliability theory, the multi-state characteristics of complex systems cannot be represented, and neither the relations between the system performance and the component performance nor the relations between the system reliability and the system performance can be reflected. Therefore, the engineering requirements for reliability analysis and optimal design of complex systems cannot be fulfilled. The multi-state system theory can describe the relations between the system performance and the component performance, the change of the system performance and the multi-state characteristics. The multi-state system theory provides a feasible approach for reliability analysis and optimal design of complex systems. At present, the researches on the multi-state system theory are mainly theoretical work, and practical problems are unable to be solved which have the characteristics of multiple performance parameters, common cause failures, and small sample.Aimed at the engineering application requirement for reliability analysis and optimal design of complex systems and the theory requirement for improvement of the multi-state system theory, this dissertation carries on a systemic research, including state definition of components, structure function analysis, reliability analysis of multi-state systems, and reliability optimization of multi-state systems. Methods to analyze the system reliability and to optimize the system structure are proposed based on the multi-state system theory. The main contributions of this dissertation are summarized as follows:1. Methods for state definition and state probabilities estimation of multi-state components are researched.Based on the characteristics of multi-state components, methods for state definition are researched. According to the data of the performance test, methods to estimate the state probabilities of components are proposed. The maximum likelihood estimate of the state probabilities is obtained using the maximum likelihood method when the sample of the tested component is large, and the Bayesian estimate of the state probabilities is obtained using the Bayesian approach when the sample of the tested component is very small. According to the performance degradation data, methods to define the states and estimate the state probabilities of degraded components are proposed. When the random shocks are taken into account, methods to define the states and estimate the state probabilities of degraded components are also proposed.2. Structure functions of multi-state systems are analyzed, and methods are proposed to define the structure functions.The characteristics of structure functions of multi-state systems are analyzed, and the structure functions of the typical multi-state systems are given. Based on the physical models of the systems and the state table, methods are proposed to define the structure functions.3. A method is proposed to analyze the reliability of multi-state systems containing multiple performance parameters.Aimed to overcome the shortages of the universal generating function, the vector universal generating function is proposed and the corresponding operations are defined to analyze the reliability of multi-state systems containing multiple performance parameters. The procedure for reliability analysis of multi-state series-parallel systems is provided based on the vector universal generating function. The precision and complexity of the vector universal generating function are analyzed, and methods are provided to improve the precision and simultaneously make computing easier. Moreover, the vector universal generating function of common cause groups is obtained when common cause failures are considered.4. A method is proposed to analyze the interval-valued reliability of multi-state systems based on the interval analysis theory.When state performance levels and/or state probabilities of components are imprecise, the interval universal generating function is introduced to analyze the interval-valued reliability of multi-state systems. The interval universal generating function is developed and the corresponding operations are defined. Given the interval-valued state performance levels and state probabilities of components, a method is proposed to analyze the interval-valued reliability of multi-state systems. Because of the dependence problem in interval arithmetic, the interval-valued reliability obtained by the interval universal generating function method is overestimated compared with the exact value. Therefore, affine arithmetic is introduced, and the affine universal generating function is presented to solve the dependence problem and to improve the interval-valued reliability.5. Reliability optimization of multi-state systems subject to common cause failures and interval-valued reliability optimization of multi-state systems are studied.The single objective optimization model and the multi-objective optimization model of multi-state systems are provided. The genetic algorithm is modified, and the hybrid genetic algorithm is proposed. The structures of multi-state systems subject to common cause failures are optimized. The operator of intervals ordering is defined, and the optimization of the interval-valued reliability of multi-state systems is researched.6. The reliability of a power system is analyzed, and the structure of the power system is optimized. The interval-valued reliability of the system is also analyzed.A system illustrates the proposed methods in this dissertation. The reliability of the power system is analyzed by both the multi-state system theory and the traditional method. The results obtained by the multi-state system theory are almost the same as the exact values, while the results obtained by the traditional method are always conservative. The structure of the power system is optimized, and optimal structures are obtained. According to the test data of subsystems, the interval-valued reliability of the whole system is analyzed.In summary, with the aid of the National High Technology Research and Development Program and supported by the Graduate School of National University of Defense Technology, the multi-state system theory is improved, and the procedures are proposed to analyze the reliability and optimize the structures of complex systems based on the multi-state system theory. The research work in this dissertation is very important and valuable for the development and application of the multi-state system theory, and provides a feasible approach for reliability analysis and optimal design of large complex systems and important products.