This paper illustrates haw $Y_2O_3$ contributes to crack-healing strengths as a function of crack-healing temperature and the additive amount. In investigating mechanical properties, the indentation fracture method is very simple and useful, but careful attention must be paid to the statistical data processing because data may be scattered excessively, especially for brittle materials. To estimate accurate AE signal properties we applied the useful time-frequency method with a discrete wavelet analysis algorithm. In experiments, three kinds of specimens were prepared. After the specimens were indented by a Vickers indentor, they were heat-treated and crack-healed to evaluate bending strength and the AE signal. With higher amounts of the additive powder, as 1, 3, or 5% wt. of $Y_2O_3$, the concentrative tendency of dominant frequency trended toward lower frequency groups. The $Al_2O_3$ ceramic with 3% wt. of $Y_2O_3$ was judged most suitable because it demonstrated superior crack-healing ability and relative concentration on the highest frequency group.