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This paper investigates the defect formed by the mechanical cutting processing of green sheet of alumina ceramic by evaluating the surface integrity in terms of surface morphology, and the flexural strength and its variance. The Weibull strength distribution method is introduced to compare the strength between defect-contained specimens and specimens without hot-cutting defect. Experimental results show that the defect causes a remarkable decline in strength and small specimens are more affected than big ones. The surface contains the hot-cutting defect is more dangerous than the natural surface. A FEM method (ANSYS) is utilized to quantitatively evaluate residual stresses of the ceramic insulator in brazing process. Based on the stress analysis, a Defect-free-stress design concept is put forward to give some guidance to structure design and material selection.