Joining Si3N4 and Al2O3 using 15 layers has been achieved by a unique approach that introduces SiAlON polytypoids as a functionally graded material (FGM) bonding layer. Previously, the hot press sintering of multilayered FGM with 20 layers, each 500 µm thick, has been achieved successfully. In the present study, the number of layers for FGM was reduced from 20 to 15 to increase optimization. Samples were fabricated by hot pressing at 48 MPa during the temperature ramp to 1650°C and cooling at 2°C/min to minimize residual stresses from sintering. Moreover, a finite element method (FEM) program based on the maximum principal stress theory and the maximum tensile stress theory was applied to design optimized and reduced FGM layers that produced a crack-free joint. The sample had a 3-dimensional cylindrical shape that was transformed to a 2-dimensional axisymmetric mode. By determining the expected thermal stress from the calculated elastic modulus and coefficient of thermal expansion, we were able to predict and prevent damage due to thermal stresses. These analyses are especially useful for FGM samples where it is very difficult to measure the residual stresses experimentally. Finally, oriented Vickers indentation testing was used to qualitatively characterize the strengths of the joint and the various interfaces. The indentation cracks were deflected at the SiAlON layers, implying weak interfaces. In other areas, cracks were not deflected, implying strong interfaces.