Table 6E.4 presents 20 subgroups of five measurements on the critical dimension of a part produced by a machining process. Table 6E.4 Data for Exercise 6.9 Sample Number X5 7 R 1 138.1 110.8 138.7 137.4 125.4 130.1 27.9 2 149.3 142.1 105.0 134.0 92.3 124.5 57.0 3 115.9 135.6 124.2 155.0 117.4 129.6 39.1 4 118.5 116.5 130.2 122.6 100.2 117.6 30.0 5 108.2 123.8 117.1 6 128.5 42.7 102.8 112.0 135.0 135.0 145.8 126.1 43.0 142.4 150.9 7 120.4 84.3 112.8 118.5 119.3 111.0 36.1 8 132.7 151.1 124.0 123.9 105.1 127.4 46.0 9 136.4 126.2 154.7 127.1 173.2 143.5 46.9 10 11 139.6 127.9 151.1 12 125.3 160.2 130.4 135.0 115.4 149.1 138.3 130.4 143.7 110.5 152.4 133.6 33.7 134.6 40.6 165.1 146.7 39.8 13 145.7 101.8 14 15 16 141.1 138.1 9.2 110.1 114.6 165.1 113.8 139.6 128.7 54.8 145.2 101.0 154.6 120.2 117.3 127.6 53.3 149.5 113.3 151.8 132.4 50.0 138.6 139.0 131.9 140.2 17 18 19 20 20 125.9 135.3 121.5 147.9 105.0 127.1 42.9 129.7 97.3 130.5 109.0 150.5 123.4 53.2 123.4 150.0 161.6 148.4 154.2 147.5 38.3 144.8 138.3 119.6 151.8 142.7 139.4 32.2 a. Set up xbar and R control charts on this process. Verify that the process is in statistical control. b. Following the establishment of control charts in part (a) above, 10 new samples in Table 6E.5 were collected. Plot the xbar and R values on the control chart you established in part (a) and draw conclusions. Table 6E.5 Additional Data for Exercise 6.9, part (b) Sample Number 4 12 14 X R 1 131.0 184.8 182.2 143.3 212.8 170.8 81.8 2 181.3 193.2 3 154.8 180.7 169.1 174.3 170.2 168.4 202.7 174.4 4 157.5 5 216.3 154.2 174.3 169.1 166.2 179.7 24.0 174.1 48.0 142.2 161.9 157.0 26.9 155.5 184.3 179.3 60.8 6 186.9 180.2 149.2 175.2 185.0 175.3 37.8 7 167.8 143.9 157.5 171.8 194.9 167.2 51.0 8 178.2 186.7 142.4 159.4 167.6 166.9 44.2 9 162.6 143.6 132.8 168.9 177.2 157.0 44.5 10 172.1 191.7 203.4 150.4 196.3 182.8 53.0 c. Suppose that the assignable cause responsible for the action signals generated in part (b) has been identified and adjustments made to the process to correct its performance. Plot the xbar and R values from the new subgroups shown in Table 6E.6, which were taken following the adjustment, against the control chart limits established in part (a). What are your conclusions? Table 6E.6 New Data for Exercise 6.9, part (c) Sample Number X3 X R 1 2 111.0 127.3 3 129.8 98.3 110.4 91.0 134.0 105.1 4 145.2 132.8 106.1 131.0 131.5 143.1 118.5 103.2 121.6 123.6 39.8 143.9 116.7 52.8 133.1 120.1 35.7 99.2 122.8 46.0 5 114.6 111.0 108.8 177.5 121.6 126.7 68.7 6 125.2 86.4 64.4 137.1 117.5 106.1 72.6 7 145.9 109.5 84.9 129.8 110.6 116.1 61.0 8 123.6 114.0 135.4 83.2 107.6 112.8 52.2 9 85.8 156.3 10 107.4 148.7 119.7 96.2 153.0 122.2 70.6 127.4 125.0 127.5 127.2 41.3