**Abstract**

The surfaces of fiber woven composites (FWCs), especially woven ceramic matrix composites (WCMCs), are obviously anisotropic. Many kinds of damage, which are different from traditional homogeneous materials, could be caused by the fabrication and machining process. The old surface evaluation system appropriate for isotropic materials is no longer suitable to WCMCs, thus causing many difficulties in terms of their wide industrial applications. This chapter presents a grading surface measurement and evaluation system for WCMCs based on their microstructures. The system includes four levels: fiber, fiber bundle, cell body, and the whole surface. On the fiber level, the typical forms of fiber damage, and their effects on the surface morphology of WCMCs are analyzed, which lays a foundation for the measurement and evaluation methods on the next three levels. On each subsequent level, the system proposes a set of surface measurement sampling parameter determination methods and surface quality evaluation methods based on the principle of statistics. As demonstrations, the surface measurement and evaluation on each level were processed on a carbon fiber-reinforced silicon carbide matrix composite (Cf/SiC) to illustrate the methodology of the system.

**Keywords:** woven ceramic matrix composites, grading surface evaluation, surface sampling method, confidence interval, residual error estimate
