Reliability Estimation Of Stress Strength Model Of Transmuted Weibull Distribution

The stress strength model,also known as the failure physical model,was first proposed by Birnbaum in 1956.There are related applications based on this model in the fields of hydraulic engineering,architecture,mechanics and so on.Weibull distribution is a popular distribution in the field of reliability research.The Transmuted Weibull distribution is obtained by the quadratic rank transmutation mapping of the two-parameter Weibull distribution.This paper focuses on the reliability estimation of the stress strength model based on the Transmuted Weibull distribution.Firstly,the expressions of the Weibull distribution and the Transmuted Weibull distribution are introduced,and the influence of parameter changes on the probability density of the Transmuted Weibull distribution is analyzed.Secondly,the expression of the reliability of the stress strength model is derived.Thirdly,some related theorem definitions and the basic ideas of maximum likelihood estimation(MLE)and Bayes estimation are introduced.For the point estimation and interval estimation of reliability,Both MLE and Bayes estimation methods are used.In the MLE of reliability,Newton iteration method is used.In the Bayes estimation of reliability,Lindley algorithm and MCMC algorithm are used.The simulation part is carried out using Matlab programming.The other is the maximum posterior probability density interval is referred to as the HPD interval,For the point estimation of reliability,compare the calculated risk function,and analyze the point estimation effect of different estimation methods in the simulation experiment.For the interval estimation,MLE obtains confidence interval,and then two algorithms are used to find the interval of Bayes estimation.One is the asymptotic confidence interval,based on the Lindley algorithm;The other is HPD interval,based on the MCMC algorithm.Calculate the length of the interval,compare the size of the length,and analyze the interval estimation effect of different estimation methods in the simulation experiment.At last,two examples are introduced.The Transmuted Weibull distribution stress strength model is applied to two examples.The MLE and Bayes estimation are used to obtain the point estimation and interval estimation results of the reliability,which shows the feasibility of the reliability of the Transmuted Weibull distribution stress strength model in real life.