SELECTION OF A BETTER COMPONENT IN BIVARIATE EXPONENTIAL MODELS DAVID D. HANAGAL Department of Statistics, University of Poona, Pune-411007, INDIA. Visiting Professor, Departamento de Estadistica, Colegio de Postgraduados-Montecillo, Texcoco, CP56230, MEXICO. ABSTRACT Selection procedures of the better component in bivariate exponential (BVE) models are proposed. In this paper, we consider only BVE models proposed by Freund (1961) Marshall-Olkin (1967) and Block- Basu (1974). The probabilities of correct selection for the proposed procedures are compared by using the normal approximations. A numerical study on the determination of asymptotic relative efficiency (ARE) of the proposed procedures are presented. Key words and Phrases: Asymptotic Relative Efficiency, Better component, Bivariate exponential, Probability of correct selection, Selection procedures. AMS (1990) Subject Classification Number: 62F03. 1. INTRODUCTION In this paper, we are interested to know the component which has longer mean life time between the two dependent components in a parallel system. The component which has longer mean life time is called as a better component. If ¯ X 1 and ¯ X 2 are the sample mean lifetimes of the two components C 1 and C 2 respectively. We select C 1 as the better component when ¯ X 1 > ¯ X 2 otherwise we select C 2 . Assuming the component C 1 is selected, the probability of correct selection(CS) is P [CS ]= P [ ¯ X 1 − ¯ X 2 > 0]. We consider the life times (X 1 ,X 2 ) of two components follow bivariate exponential (BVE) distribution proposed by Marshall-Olkin (1967), Block-Basu (1974) and Freund 1