Reliability Estimation Of Stress Strength Model For Generalized Inverse Weibull Distribution

The stress intensity model was proposed by Birnbaum(1956).It is widely used in engineering,medicine,psychology and other fields.Especially in engineering,it is an important content to study the quantitative relationship between stress and strength in the life test and reliability analysis of mechanical products.Considering from the point of view of mathematical statistics,the probability description and generalization of this quantitative relationship can be used to solve the parameters under different distribution assumptions.The problem of estimation is of great significance.Weibull distribution is a common product failure distribution.Generalized inverse Weibull distribution is a generalization of Weibull distribution.This paper mainly considers the reliability estimation of stress intensity model with generalized inverse Weibull distribution.Firstly,it is assumed that the strength variables and the stress variables in the stress intensity model are independent of each other and obey the generalized inverse Weibull distribution.Secondly,according to the relationship between the distribution parameters of the two variables and the reliability of the model,the point estimation and interval estimation of the reliability are studied.For point estimation,a sufficiently small positive number is introduced into the conventional Newton iteration algorithm,and a set of suitable parameter sequences is constructed to satisfy the monotonic increment of logarithmic likelihood function.An improved reliability maximum likelihood estimation is obtained through the modified iteration operation.On the other hand,Bayes estimation of reliability is obtained by using Lindley approximation algorithm and MCMC algorithm.The mixed extraction of MH and Gibbs is used in MCMC algorithm.For interval estimation,according to the asymptotic normality of maximum likelihood estimation and Bayes estimation,the asymptotic confidence intervals of reliability based on these two estimation methods are given.Secondly,the maximum posterior probability density(HPD)interval of reliability is obtained by using MCMC algorithm.In the following stochastic simulation process,the simulation results of the two estimates are compared by calculating the risk function of reliability maximum likelihood estimation and Bayes estimation.For interval estimation,the interval accuracy of the two estimates is compared according to the calculation results of asymptotic confidence interval and HPD interval length.Finally,maximum likelihood estimation and Bayes estimation based on Lindley algorithm and MCMC algorithm are applied to specific examples,and point estimation and interval estimation of single carbon fiber reliability are obtained,which verify the feasibility of the two estimation methods.