Contact-connection matrix is proposed to describe contact and connection relations between components. Extended interference matrix is given to settle non-orthogonal assembly problems effectively which other current methods are incapable of. Several rules that influence the efficiency of assembly are studied from the quantification point of view. The priorities of the rules can be customized to screen optimum components in every cyclic process to comprise an optimized sequence automatically, using the above matrices. The prototype system is developed on UG NX platform and a fixture with 30 parts containing tilt assembly directions is demonstrated as an example. The results indicate that the algorithm is efficient and flexible.