  To understand the dynamical origin of the measurement in quantum mechanics,
several models have been put forward which have a quantum system coupled to an
apparatus. The system and the apparatus evolve in time and the Born rule for
the system to be in various eigenstates of the observable is naturally
obtained. In this work, we show that the effect of the drive-induced
dissipation in such a system can lead to the Born rule, even if there is no
separate apparatus. The applied drive needs to be much stronger than the
system-environment coupling. In this condition, we show that the dynamics of a
driven-dissipative system could be reduced to a Milburn-like form, using a
recently-proposed fluctuation-regulated quantum master equation [A. Chakrabarti
and R. Bhattacharyya, Phys. Rev. A 97, 063837 (2018)]. The system evolves
irreversibly under the action of the first-order effect of the drive and the
drive-induced dissipation. The resulting mixed state is identical to that
obtained by using the Born rule.
