Systematic behavior of decay rates of resonances above dissociation threshold is investigated by using the theory of resonance scattering. The condition for the Rice-Ramsperger-Kassel-Marcus (RRKM) rate formula to be valid is clarified by analyzing the random model of unimolecular dissociation. The decay rate averaged over many resonances agrees with the RRKM rate when the mean spacing and the mean width of the resonance states coincide with each other. On the other hand, auto- and mutual-correlation functions of the non-stationary wave functions indicate a rather paradoxical and intriguing phenomenon: In the RRKM regime, insufficient time is left for intramolecular vibrational energy redistribution (IVR) before dissociation.