3. Reconsider the situation in Exercise 11.2. Suppose that the sample mean vector and sample covariance matrix provided were the actual population parameters. What control limit would be appropriate for phase II of the control chart? Apply this limit to the data and discuss any differences in results that you find in comparison to the original choice of control limit. 11-2 p=3 A product has three quality characteristics. The nom- inal values of these quality characteristics and their X 3.0 3.1 sample covariance matrix have been determined from the analysis of 30 preliminary samples of size 1 = 10 as follows: 13.00 11.40 1.02 1.05 X = 3.5 S= 1.02 1.35 0.98 2.8 1.05 0.98 1.20 The sample means for each quality characteristic for 15 additional samples of size n = 10 are shown in Table 11E 2. Is the process in statistical control? - TABLE 11 E.2 Data for Exercise 11.2 Sample Number X; 1 2 3.3 3.9 3 2.6 30 4 2.8 3.0 S 3.0 3.3 6 4.6 7 3.8 4.2 8 3.3 9 2.4 3.0 10 2.6 11 3.2 3.9 12 3.7 4.0 13 4.1 4.7 14 3.8 4.0 15 3.2 3.6 4.0 2.4 2.5 2.8 3.5 3.0 2.7 2.2 1.8 3.0 2.0 3.0 3.0 2.9 2.8 11-2 Opboard C D E Styles N F G M O P 1 p B 3 30 10 0.003 55793 Alignment H xdoublebars 3 3.5 28 Number J K S: Var.Covar Matrix 1.4 1.02 1.02 1.35 1.05 0.98 1.05 0.98 1.2 2.3084 -0.6824 -1.4625 -0.6824 2.0210 -1.0534 -1.4625 - 1.0534 2.973) alpha ONO 7 Sample No. 1 2 3 4 5 6 7 8 9 11 12 13 14 15 3.1 26 2.8 2 4 3.8 3 2.4 3.2 3.7 4,1 3.8 3.2 9 bara 3.7 3.9 3 3 3.3 4.6 42 33 3 2.6 3.9 4 4.7 4 3.6 10 bar 3.1 2.4 2.5 2.8 35 3 2.3 22 1.8 3 3 3.2 2.9 2.8 11 12 M 0.1 0.2 -0.4 -0.2 0 1 0.8 0 0,6 - 1 0.2 0.7 0.8 13 dift2 02 02 1.1 044 -0.5 -0.5 -0.2 1.1 0.7 0.2 0.5 -0.9 14 0.4 0.5 1.2 0.2 0.1 05 0.3 -0.4 03 0 0.7 02 -0.1 -0.6 0.2 02 15 0.4 0.1 0 18 matrical 0.0528 0.1189 0.163 02372 0.0803 1.0997 1.0593 0.004 0.3122 0.1692 0.1399 0.6574 IT 12cale 0.5279 1.800 2.0793 23719 0.1084 10.3966 1.1271 0.0852 10.5932 0.6844 3.1216 86922 1.1990 65741 10 20.7927 11.2706 08525 19 UCL 174251 17.4251 174251 174251 174251 174251 17.4251 17.4251 17.4251 LCL 17.4251 17.4251 17 4251 D 0 17.4251 17.4251 17.4251 0 0 0 o D O 0 0 11 000 0 In control in control in control in control control in control in control 0 In control in control in control in control in control Above UCL In control in control 0 0 3 M 25 =MMULT(MMULT(TRANSPOSE(B12:B14),SNS 2:$P$4),B12:314) T^2 Control Chart for Quality Characteristics 25 20 15 T^2 10 5 0 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Sample Number -UCL -t2-n calc-LCL =