Mean Remaining Strength Estimation Of System Based On Nonparametric Bayesian Method

The mean remaining strength estimation is the premise of system security work,which can reduce the frequency and cost of detection work and provide guarantee for system intelligent detection.Stress-strength system is a widely existed model.It is necessary to analyze the residual strength of components and systems.Since the strength distribution of new products is usually unknown,it brings challenges to the traditional distribution-based parameter estimation methods.In this paper,the nonparametric Bayesian estimation method of mean remaining strength of stress-strength system is studied from two aspects of component strength independence and dependence.The main works and results are as follows:(1)The multi-state stress-strength system composed of two-state components is discussed,and the mean remaining strength of the system under different states is estimated.Based on multidimensional signature,the multidimensional signature of the strength system is derived,and the mean remaining strength of the system under different states is studied.In order to verify the rationality and applicability of nonparametric Bayesian estimation method,simulation analysis and actual cases based on fiber strength data set are given respectively.In the simulation,the relative bias,root mean square error and bootstrap confidence interval are used as the evaluation indexes.The results show that the nonparametric Bayesian estimation method has smaller evaluation index value and better effect than the nonparametric maximum likelihood estimation method.(2)The mean remaining strength of strength dependent system is estimated by nonparametric Bayesian estimation method.The copula theory is used to establish the dependence relation between component strengths,and the expression of the mean remaining strength of the system is obtained.The Monte Carlo simulation of series system and parallel system data verifies the effectiveness of nonparametric Bayesian estimation method.The fiber strength data were applied and analyzed.The results show that the estimation effect of nonparametric Bayesian estimation method is better than that of nonparametric maximum likelihood estimation method.In the case of component strength dependent,the effect of dependencies between system components cannot be ignored in practical applications.In summary,it is reasonable to estimate the mean remaining strength of the system by nonparametric Bayesian estimation method,which provides a new idea for estimating the mean remaining strength of the stress-strength system.For the multi-state system with independent component strength,a simple and reasonable method to judge the state of the system is given compared with the complex definition of multi-state components.For the strength dependent system,compared with the mean remaining strength under the independent assumption,the strength model considering the dependence between components is given.The research results provide theoretical reference and practical guidance for intelligent system life prediction.