This paper is devoted to discuss the stress-strength reliability model R = Pr (Y < X) when X and Y have an exponentiated
generalized inverse Weibull distribution (EGIW) with different parameters. The problem of stress-strength reliability is studied to
obtain estimates of a component reliability function of EGIW distribution. Reliability for multi-component stress-strength model for
EGIW distribution is also studied. Maximum likelihood estimation for stress-strength reliability of underlying distribution is
performed. Bayesian estimator of R is obtained using importance sampling technique. A simulation study to investigate and compare
the performance of each method of estimation is performed. Finally analysis of a real data set has also been presented for illustrative
purposes.