The shortcomings of continuum damage mechanics (CDM) are discussed and non-equilibrium statistical physics is used to establish a new statistical theory of inhomogeneous damage. The initiation and growth of microscopically damaged regions (cracks, voids, etc.) is regarded as the elementary process of damage to the material structure and the accumulation damage, i.e. damage variable, is universally defined as the failure probability of the material due to the initiation and growth of the microscopically damaged regions. From the statistical evolution equation of damaged regions, and the minimum strength principle, a partial differential equation, which universally describes the evolution of damage parameter, is found. Not only can this equation characterize the kinetic process of damage evolution, but it can also establish the relationships between the microbehaviour of damage (the initiation and growth of the microscopically damaged regions and the statistical consequences of damage) and the degradation of material properties. Finally, as an example, the newly developed theory is applied to study the time-dependent fracture of Al2O3 ceramic. The effects of structural inhomogeneity on mechanical properties of the material is discussed.