Suppose there are two groups of random variables, one with independent and non-identical distributed and another with independent and identical distributed. In this paper, for the case when the size of groups are not equal, and all of the underlying random variables have exponential distribution, the necessary and sufficient conditions are obtained for establishing the mean residual life, hazard rate and dispersive orders between the second order statistics of two groups. Moreover, when random variables follow the Weibull distribution, the hazard rate, dispersive and likelihood ratio order between the second order statistics from two groups are investigated.