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}tleq$10$^{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.
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