INFERENCE PROCEDURES FOR A BIVARIATE EXPONENTIAL MODEL OF GUMBEL BASED ON LIFE TEST OF COMPONENT AND SYSTEM

Based on life test experiments conducted at both component and (series) system levels, we develop inference procedures for a bivariate exponential distribution of Gumbel. For the case of identical marginals, maximum likelihood estimators are obtained in closed form and their asymptotic properties are presented. Some nonstandard conditions arise due to the restricted form of the parameter space. Exact optimal test and confidence bounds are provided for the model parameters as well as series system reliability. For testing the equality of marginals, we derive an asymptotically best combination of two test statistics each of which provides optimal test when only a part of sufficient statistics is observable.