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Our two types of NOx storage-reduction (NSR) catalyst have been tested under various conditions of thermal endurance; the performance of these catalysts have been regressed to give the formulas that enable to estimate the performance after thermal endurance; and we have found the method to simplify (shorten the duration of) the thermal endurance tests and that the thermal deterioration of NSR catalysts is controlled by the worst condition of endurance (at least approximately). The regression formula for the amount of potassium that contributes to the catalyst performance (active K) after the endurance has also been obtained. These formulas predict that the amount of active K is the least for the worst condition of endurance and suggest a difference in deterioration mechanism that reflects the performance between low and high temperatures and the portion of worse deterioration (front or rear).