The purpose of this paper is to provide information for the characterization of the products and feed of a crude fractionator, hard to get from a hardware system, by using probability function and inferential model of realtime operating conditions. TBP is a major characteristic of CDU products and feed. It has become possible to consider that the TBP of component can be predicted by using an inferential modeling technique such as partial least square (PLS) or artificial neural network. On the other hand, knowing that the characteristic of each product of a crude distillation unit follows a continuous probability distribution function, variables of the probability distribution function can be calculated from operating conditions in the same way. In general, the proposed model can provide a tool for doing more efficient operations to maximize profit.