Bayesian Estimation Of Stress-strength Model With Outliers

The Stress-strength model is widely used in the reliability evaluation of mechanical devices and electrical components,in the Stress-strength model,the stress is defined as the load that causes the device or component to fail,and the strength is defined as the ability of the device or component to satisfactorily perform the specified task without failure when subjected to an external load,the reliability parameter is defined as the probability that the stress that affects the failure does not exceed the strength that controls the failure.In this thesis,we study the Stress-strength model in the Rayleigh distribution with presence of two outliers.To describe the problem in mathematical language,that is to say,we study the problem of estimating the reliability parameter R = P(Y < X),where Y represents the stress and has Rayleigh distribution with parameter ?,X represents the strength and has Rayleigh distribution in the presence of two outliers with parameters ? and ?,such that X and Y are independent.Foreign scholars on the study of Stress-strength model that with outliers usually use classical methods.Domestic scholars on the study of Stress-strength model almost do not consider the situation that the sample contains outliers.In this thesis,the estimation of R is studied by Bayesian method,compared to classical methods that consider the unknown parameter as a constant,Bayesian method considers the unknown parameters as random variables,the statistics inference is made by using the information of sample distribution and prior distribution.In this thesis,Bayesian estimation will be given under three loss functions: square loss,0-1 loss and symmetric entropy loss.Then according to the results,bias of these estimators are given with the help of numerical techniques,then we compare these Bayesian estimators,then we can get the final conclusion,it is an effective way to use Bayesian method to study the Stress-strength model with outliers.