Preservation of generalized ageing classes on the residual life at random time

► We show that if Y is DRHR and X is s-IFR, then XY is s-IFR. ► We show that if there exists an exponential random variable Y such that XY is s-IFR, then X is (s+1)-IFR. ► Some characterizations of s-IFR (s-DFR) ageing class are derived on XY. ► The bounds of XY are obtained when Y is an exponential random variable.