Six-Sigma has some measures which measure performance characteristics related to a process. In most of the traditional methods, exact estimation is used to assess these measures and to utilize them in practice. In this paper, to estimate some of these measures, including Defects per Million Opportunities (DPMO), Defects per Opportunity (DPO), Defects per unit (DPU) and Yield, a new algorithm based on Buckley's estimation approach is introduced. The algorithm uses a family of confidence intervals to estimate the mentioned measures. The final results of introduced algorithm for different measures are triangular shaped fuzzy numbers. Finally, since DPMO, as one of the most useful measures in Six-Sigma, should be consistent with costumer need, this paper introduces a new fuzzy method to check this consistency. The method compares estimated DPMO with fuzzy customer need. Numerical examples are given to show the performance of the method. All rights reserved.