  The disk fraction, the percentage of stars with disks in a young cluster, is
widely used to investigate the lifetime of the protoplanetary disk, which can
impose an important constraint on the planet formation mechanism. The
relationship between the decay timescale of the disk fraction and the mass
dissipation timescale of an individual disk, however, remains unclear. Here we
investigate the effect of the disk mass function (DMF) on the evolution of the
disk fraction. We show that the time variation in the disk fraction depends on
the spread of the DMF and the detection threshold of the disk. In general, the
disk fraction decreases more slowly than the disk mass if a typical initial DMF
and a detection threshold are assumed. We find that, if the disk mass decreases
exponentially, {the mass dissipation timescale of the disk} can be as short as
$1\,{\rm Myr}$ even when the disk fraction decreases with the time constant of
${\sim}2.5\,{\rm Myr}$. The decay timescale of the disk fraction can be an
useful parameter to investigate the disk lifetime, but the difference between
the mass dissipation of an individual disk and the decrease in the disk
fraction should be properly appreciated to estimate the timescale of the disk
mass dissipation.
