This work discusses and proposes the construction principles of particle concentration-based mixing indices for a general particle system. The principles proposed herein follow the criteria and advantages of scalability, flexibility, reliability, applicability, and a wide range of applications. Following the current principles, a series of new mixing indices are proposed. The new mixing indices for a simple particle system and for the axial mixing cases of cubic particles in the tilted tumbler are calculated and verified by comparing them with classic mixing indices. As a demonstrative application, the mixing phenomenon of particles in a tilted tumbler are simulation by SIPHPM simulation and evaluated by the new mixing indices.