Reliability Analysis And Optimization Of Complex Systems Under Small Sample Conditions

System reliability is an important part of reliability theory,and it is the most basic and important problem in system performance assurance.The advancement of science and technology makes the structure of the system more and more complicated.At the same time,the characteristics of "high reliability and less failure" make the traditional statistical research method based on large sample failure data no longer suitable for small sample cases,how to accurately and efficiently perform system reliability analysis and optimization under small sample conditions is one of the important issues to be solved in the current reliability field.Therefore,it is necessary to carry out reliability analysis and optimization research of complex systems in small samples.The specific work is as follows:(1)Research on the reliability analysis methods with small samples.In view of the shortage of sample data,several commonly used reliability analysis methods for small samples are studied and analyzed,and the application and selection principles of different methods are discussed.On this basis,the uncertainty caused by the shortage of small sample reliability analysis method and the shortage of sample data is quantified by introducing P-Box theory,and the calculation method of P-Box is discussed.On this basis,the influence of P-Box on the number of samples is analyzed.(2)Reliability and sensitivity analysis of complex systems with small samples.Based on Survival signature and P-Box method,the reliability analysis of complex systems with small samples is carried out to represent the system reliability in the form of interval reliability function,and the uncertainty at the system level is quantitatively analyzed.On this basis,the formula for calculating the reliability of a system with precise probability distribution is derived.Secondly,the relative importance index theory is used to analyze the importance of components,and based on Survival signature and P-Box,the sensitivity analysis method of components under small samples is derived.(3)Reliability optimization analysis of complex systems with small samples.A new intelligent optimization algorithm-Stochastic Fractal Search algorithm was introduced,and a new system reliability redundancy allocation model was established based on Survival signature,which optimized and calculated system reliability,component reliability and redundancy,and determined the installation location of redundant components according to the optimization results and component importance level.Finally,the reliability optimization analysis of the auxiliary power supply system of the auxiliary power supply system for CRH3 EMU is carried out to verify the correctness and rationality of the theory and method described in this paper.