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Engineering Statistics Handbook Episode 8 Part 9

Tham khảo tài liệu 'engineering statistics handbook episode 8 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 6.3.4.3. Multivariate EWMA Charts ENGINEERING STATISTICS HANDBOOK hW tools raids lỉEÂtCH BACK Nixf 6. Process or Product Monitoring and Control 6.3. Univariate and Multivariate Control Charts 6.3.4. What are Multivariate Control Charts 6.3.4.3. Multivariate EWMA Charts Multivariate EWMA Control Chart Univariate EWMA model Multivariate EWMA model Illustration of multivariate EWMA The model for a univariate EWMA chart is given by Zị AXj 1 - AJZj.j 1 1 2 . n where Zi is the ith EWMA Xi is the the ith observation Zo is the average from the historical data and 0 À 1. In the multivariate case one can extend this formula to Zi AXi4- l-A Zi_1 where Zị is the ith EWMA vector Xi is the the ith observation vector i 1 2 . n Zo is the vector of variable values from the historical data A is the diag 2 . p which is a diagonal matrix with J 1 J 2 . Àp on the main diagonal andp is the number of variables that is the number of elements in each vector. The following illustration may clarify this. There are p variables and each variable contains n observations. The input data matrix looks like The quantity to be plotted on the control chart is http www.itl.nist.gov div898 handbook pmc section3 pmc343.htm 1 of 4 5 1 2006 10 35 06 AM Simplification It has been shown Lowry et al. 1992 that the k Z th element of the covariance matrix of the zth EWMA Sij is 6.3.4.3. Multivariate EWMA Charts Table for The following table gives the values of 1-A 2i for selected values of A selected and i. values of A and i 1 - A 4 6 8 10 2i 12 20 30 40 50 .9 .656 .531 .430 .349 .282 .122 .042 .015 .005 .8 .410 .262 .168 .107 .069 .012 .001 .000 .000 .7 .240 .118 .058 .028 .014 .001 .000 .000 .000 .6 .130 .047 .017 .006 .002 .000 .000 .000 .000 .5 .063 .016 .004 .001 .000 .000 .000 .000 .000 .4 .026 .004 .001 .000 .000 .000 .000 .000 .000 .3 .008 .001 .000 .000 .000 .000 .000 .000 .000 .2 .002 .000 .000 .000 .000 .000 .000 .000 .000 .1 .000 .000 .000 .000 .000 .000 .000 .000 .000 Simplified It should be .