In this note, we study the paper of Chung and Lin that published in Computers & Operations Research. It is an important paper that proved that the total cost is convex with respect to the number of partitions such that it solved the problem when to stop the numerical testing. However, there are only three papers quoted this important paper in their references. It may be that the complicated proof hindered ordinary readers realize and absorb their paper. The purpose of this note is twofold. First, we explain why their method looks so complicated. Second, we offer some easy proofs for their lemma to help ordinary readers to digest their theorem. Our finding will help ordinary readers to absorb and utilize this important paper.