  Recently it was shown that cosmic anisotropy can be well tested using either
standard siren measurement of luminosity distance $d_\mathrm{L}(z)$ from
gravitational-wave (GW) observation or dispersion measure ($\mathrm{DM}(z)$)
from fast radio burst (FRB). It was also observed that the combined measurement
of $d_\mathrm{L}(z)\cdot\mathrm{DM}(z)$ from the GW/FRB association system as
suggested in some of FRB models is more effective to constrain cosmological
parameters than $d_\mathrm{L}(z)$ or $\mathrm{DM}(z)$ separately due to its
independence from Hubble constant. In this paper, we will show both
theoretically and with simulation that, this upgraded sirens from combined
GW/FRB observations could test cosmic anisotropy with a double relative
sensitivity compared to the usual standard siren from GW observation alone.
