Private processes are the basis for building a collaborative business process

and its correctness has a direct impact on the business collaboration implementation. To this end

we propose an approach of step-by-step refinement to build a private process. First

we define a private process and abstract its control flow into four basic blocks

i.e.

sequential block

concurrent block

selection block

and iteration block. Then

we propose corresponding refinement rules for the four basic blocks

and a private process construction method is proposed based on these refinement rules. Finally

we theoretically prove that the private process established by the present approach has the characteristics of workflow network and is correct. We model the supply chain in collaborative manufacturing and compare the present approach with the existing methods. The results show that the present method can more effectively model the private process with respect to the existing typical work.