Some useful properties of the nth stop-loss order and the exponential order will be given in this paper. These results will be applied to the study of losses $L\sb{i}$ (i = 1, 2,$\cdots$), L and ruin probability $\psi$(u). A relationship between the claim amount random variables and ruin probabilities will also be found. The concepts of the nth stop-loss distance and the ruin probability distance will be introduced. A formula for ruin probabilities for heterogeneous portfolios will be given.