  Shock-wave heating within the solar nebula is one of the leading candidates
for the source of chondrule-forming events. Here, we examine the possibility of
compound chondrule formation via optically thin shock waves. Several features
of compound chondrules indicate that compound chondrules are formed via the
collisions of supercooled precursors. We evaluate whether compound chondrules
can be formed via the collision of supercooled chondrule precursors in the
framework of the shock-wave heating model by using semi-analytical methods and
discuss whether most of the crystallized chondrules can avoid destruction upon
collision in the post-shock region. We find that chondrule precursors
immediately turn into supercooled droplets when the shock waves are optically
thin and they can maintain supercooling until the condensation of evaporated
fine dust grains. Owing to the large viscosity of supercooled melts,
supercooled chondrule precursors can survive high-speed collisions on the order
of $1\ {\rm km}\ {\rm s}^{-1}$ when the temperature is below $\sim 1400\ {\rm
K}$. From the perspective of the survivability of crystallized chondrules,
shock waves with a spatial scale of $\sim 10^{4}\ {\rm km}$ may be potent
candidates for the chondrule formation mechanism. Based on our results from
one-dimensional calculations, a fraction of compound chondrules can be
reproduced when the chondrule-to-gas mass ratio in the pre-shock region is
$\sim 2 \times 10^{-3}$, which is approximately half of the solar metallicity.
