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DOX1_lab_solutions

DOX1_lab_solutions - Recitation#12 and Homework#10 DOX I...

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Recitation #12 and Homework #10: DOX I Solutions OR&IE 3120, Spring 2009 Problem 1 The original data are plotted in the top row of the figure below. The alternated data are in the bottom row. The left column has boxplots, the middle column has normal plots, and the right column has plots of thickness versus observations number. Clearly, the outlier distorts the plots so much that it is difficult to see anything else that might be a problem. In the bottom, no outliers are seen, which is good. In the bottom, right plot, we see a pattern with thickness having low values on the left side and having somewhat of a sinusoidal pattern. Since examination of the data file shows that the data are ordered by run and then wafers without runs, this indicates there is some between-run or between-wafer variability that should be investigated. Note: The R specification par(mfrow=c(2,3)) puts all six plots in one figure. 10 14 18 original data -3 -1 0 1 2 3 10 14 18 Normal Q-Q Plot Theoretical Quantiles Sample Quantiles 0 50 100 200 10 14 18 Index wdata$thickness 10.3 10.5 10.7 altered data -3 -1 0 1 2 3 10.3 10.5 10.7 Normal Q-Q Plot Theoretical Quantiles Sample Quantiles 0 50 100 200 10.3 10.5 10.7 Index wdata$thickness 1
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Problem 2 We see in the output below that b μ = 10 . 5 , σ 2 u = 0 . 00146 , σ 2 v = 0 . 01057 , and σ 2 ² = 0 . 00355 . > VarCorr(chip.lme) Variance StdDev run = pdLogChol(1) (Intercept) 0.00146 0.0381 wafer = pdLogChol(1) (Intercept) 0.01057 0.1028 Residual 0.00355 0.0596 > fixef(chip.lme) (Intercept) 10.5 Since b σ v is nearly twice as large as b σ ² and nearly three times as large as b σ u , it seems the variation in thickness is due mainly to between wafer variation within runs. The next largest variation is between chips within wafers. Between run variation is relatively small.
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