As the most commonly used computer aided inspection device in precision manufacturing, coordinate measuring machines (CMM’s) have drawn extensive interests from both researchers and practitioners. Different form-fitting algorithms have been developed to process the sampling data gathered by CMM’s. The two most commonly used form-fitting algorithms, the least squares (LS) and the minimum zone (MZ), have caused a lot of controversies in their applications for evaluations of part tolerances and functions. One of the key issues in CMM applications is to study the effectiveness of the algorithms on part functions and what result will be incurred if an inappropriate algorithm is applied. Through a case study, this paper focuses on benchmarking of the least squares and the minimum zone algorithms for functional tolerance analysis. Comparisons are also conducted to study the Type I and Type II errors which could be caused by applying the least squares and the minimum zone algorithms, respectively. The final result shows that the minimum zone algorithm is better than the least squares algorithm.