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Data Analysis Machine Learning and Applications Episode 2 Part 7

Tham khảo tài liệu 'data analysis machine learning and applications episode 2 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Root Cause Analysis for Quality Management 409 to find a node sub-process with a higher support in the branch below. This reduces the time to find the optimal solution significantly as a good portion of the tree to traverse can be omitted. Algorithm 1 Branch Bound algorithm for process optimization 1 procedure TraverseTree F 2 Y sub-nodes of 7 3 for all y E Y do 4 if N X y nmax and Q X y qmin then 5 nmax N X y 6 end if 7 if N X y nmax and Q X y qmin then 8 TraverseTree y 9 end if 10 end for 11 end procedure In many real world applications the influence domain is mixed consisting of discrete data and numerical variables. To enable a joint evaluation of both influence types the numerical data is transformed into nominal data by mapping the continuous data onto pre-set quantiles. In most our applications we chose 10 20 80 and 90 quantile as they performed the best. Verification The optimum of the problem 3 can only be defined in statistical terms as in practice the sample sets are small and the quality measures are only point estimators. Therefore confidence intervals have to be used in order to get a more valid statement of the real value of the considered PCI. In the special case where the underlying data follows a normal distribution it is straight forward to construct a confidence interval. As the distribution of CP Cp denotes the estimator of Cp is known a 1 a Cp confidence interval for Cp is given by 410 Christian Manuel Strobel and Tomas Hrycej C X y2 y2 V1 f - X -1 1-ậ Cp Ĩ- Cp Ĩ V n 1 V n 1 6 For the other parametric basic indices in general there exits no analytical solution as they all have a non-centralized 2 distribution. Different numerical approximation can be found in literature for Cpm Cpk and Cpmk see Balamurali and Kalyanasun-daram 2002 and Bissel 1989 . If there is no possibility to make an assumption about the distribution of the data computer based statistical methods as the Bootstrap method are used to calculate a confidence intervals. In .