Reliability Estimation Of Stress Strength Model Of Generalized Exponential Distribution

Since the stress strength model was put forward formally,many researchers of mathematics,statistics and engineering have joined the research of this model respectively.From a statistical point of view,we can from the parameters and non-parametric two methods to study the model,the main application scope of the model of engineering machinery,bridge engineering and so on.Due to the real life of the products and parts reliability requirements are high,so forcing people to make a lot of research.The generalized exponential distribution(GED)is based on the exponential distribution of Gupta and Kundu in 1999,and has done a lot of research on this distribution.The generalized exponential distribution is one of the life distributions,which has been studied by many scholars.In this paper,we apply this distribution to the stress strength model and make the parameter estimation for the stress strength model.In this paper,we study the statistical inference of reliability when the stress and strength of random variables are independent and subject to generalized exponential distribution.We consider the point estimate and the interval estimation problem of the reliability of the stress strength model under the condition that the scale parameters are equal and the shape parameters are equal or not equal.We obtain the maximum likelihood estimation and the generalized estimate(GE)of the reliability under these three cases respectively.The relative bias and relative Mean Square Error of the reliability estimates are obtained by Monte Carlo simulation.It is found that GE has better estimation of the reliability points.For the interval estimation,we use interval 90%and 95%reliability to simulate interval estimation of reliability.It is concluded that the real coverage of the generalized confidence interval is almost the same as the nominal coverage when the sample size is small.But the real coverage of the bootstrap quantile confidence interval under the maximum likelihood method differs greatly from the nominal coverage.