  During transient events such as major solar eruptions, the plasma can be far
from the equilibrium ionization state because of rapid heating or cooling.
Non-equilibrium ionization~(NEI) is important in rapidly evolving systems where
the thermodynamical timescale is shorter than the ionization or recombination
time scales. We investigate the effects of NEI on EUV and X-ray observations by
the Atmospheric Imaging Assembly (AIA) on board Solar Dynamic Observatory and
X-ray Telescope (XRT) on board Hinode. Our model assumes that the plasma is
initially in ionization equilibrium at low temperature, and it is heated
rapidly by a shock or magnetic reconnection. We tabulate the responses of the
AIA and XRT passbands as functions of temperature and a characteristic
timescale, $n_{e}t$. We find that most of the ions reach equilibrium at
$n_{e}t\leq$10$^{12}$ cm$^{-3}$s. Comparing ratios of the responses between
different passbands allows us to determine whether a combination of plasmas at
temperatures in ionization equilibrium can account for a given AIA and XRT
observation. It also expresses how far the observed plasma is from equilibrium
ionization. We apply the ratios to a supra-arcade plasma sheet on 2012 January
27. We find that the closer the plasma is to the arcade, the closer it is to a
single-temperature plasma in ionization equilibrium. We also utilize the set of
responses to estimate the temperature and density for shocked plasma associated
with a coronal mass ejection on 2010 June 13. The temperature and density
ranges we obtain are in reasonable agreement with previous works.
