  We introduce two types of statistical quasi-separation between local
observables to construct two-party Bell-type inequalities for an arbitrary
dimensional systems and arbitrary number of measurement settings per site. Note
that, the main difference between statistical quasi-separations and the usual
statistical separations is that the former are not symmetric under exchange of
the two local observables, whereas latter preserve the symmetry. We show that a
variety of Bell inequalities can be derived by sequentially applying triangle
inequalities which statistical quasi-separations satisfy. A sufficient
condition is presented to show quantum violations of the Bell-type inequalities
with infinitesimal values of critical visibility $v_c$.
