This paper proposes new cost error measurement method and analyzes the optimistic and pessimistic cost errors statistically which is resulted from an asynchronous parallel Simulated annealing (SA) in distributed memory multicomputers. The traditional cost error measurement scheme has inherent problems which are corrected in the new method. At each temperature the new method predicts the amount of cost error that an algorithm will tolerate and still converge by the hill-climbing nature of SA. This method also explains three interesting phenomenon of he cost error analytically. So the new cost error measurement method provides a single mechanism for the occurrence of cost error and its control.