Comparison of locations or scales of two populations is a frequently studied problems in statistical inference. In distributions free settings, the problem is extended to stochastic comparisons of two random variables. A commonly used measure for this is $\zeta_1= P(X \lt Y)$ . This measure has found applications in stress-strength reliability where $X$ and $Y$ denote stress and strength variables respectively. We propose a generalized stress-strength index (SSI) which allows for relative comparisons of group effects with those of the average distribution. Various point and interval estimators are derived when group distributions are exponential. The problem of testing of hypotheses of homogeneity of SSI for several populations has been studied in detail and several parametric and nonparametric tests developed. Implementation of all procedures is done on some real data sets.