Stress-strength reliability estimation involving paired observation with ties using bivariate exponentiated...

This paper deals with the problem of maximum likelihood and Bayesian estimation of stress-strength reliability involving paired observation with ties using bivariate exponentiated half-logistic distribution. This problem is of importance because in some real applications the strength of the component is highly dependent on the stress experienced by it. A bivariate extension of exponentiated half-logistic is discussed and an expression for the stress-strength reliability is obtained. This model is also useful to analyse data having the unusual feature of having a number of pairs with tied scores, even when the scores are continuous. The maximum likelihood estimate and interval estimate of the stress-strength reliability has been developed. The Bayes estimates of the stress-strength reliability under squared error loss function are obtained using importance sampling technique. Simulation studies are conducted to evaluate the performance of maximum likelihood and Bayes estimates. Two real-life data sets are analysed to numerically illustrate the usefulness of the developed method.