  We studied the frequency and critical mass accretion rate of millihertz
quasi-periodic oscillations (mHz QPOs) using a one-zone X-ray burst model. The
surface gravity is specified by two kinds of equation of states: neutron star
(NS) and strange star (SS). The base flux, $Q_{b}$, is set in the range of 0-2
MeV nucleon$^{-1}$. It is found that the frequency of mHz QPO is positively
correlated to the surface gravity but negatively to the base heating. The
helium mass fraction has a significant influence on the oscillation frequency
and luminosity. The observed 7-9 mHz QPOs can be either explained by a heavy
NS/light SS with a small base flux or a heavy SS with a large base flux. As
base flux increases, the critical mass accretion rate for marginally stable
burning is found to be lower. Meanwhile, the impact of metallicity on the
properties of mHz QPOs was investigated using one-zone model. It shows that
both the frequency and critical mass accretion rate decrease as metallicity
increases. An accreted NS/SS with a higher base flux and metallicity, combined
with a lower surface gravity and helium mass fraction, could be responsible for
the observed critical mass accretion rate ($\dot{m}\simeq 0.3\dot{m}_{\rm
Edd}$). The accreted fuel would be in stable burning if base flux is over than
$\sim$2 MeV nucleon$^{-1}$. This finding suggests that the accreting NSs/SSs in
low-mass X-ray binaries showing no type I X-ray bursts possibly have a strong
base heating.
