Table 6E.9 presents 20 subgroups of five measurements on the critical dimension of a part produced by a machining process.

(a) Set up x 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.10 were collected Plot the x and R values on the control chart you established in part (a) and draw conclusions.

(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 x and R values from the new subgroups shown in Table 6E.11 which were taken following the adjustment, against the control chart limits established in part (a). What are your conclusions?

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TABLE 6E.9 Data for Exercise 6.20 Sample Number ri r: r, 4 r! f R 1 138.1 110.8 138.7 1374 125.4 130.1 27.9 2 149.3 142.1 105.0 134.0 923 124.5 57.0 3 5.9 135.6 124.2 155.0 117.4 129.6 39.1 4 118.5 116.5 130.2 122.6 1002 117.6 300 5 108.2 123.8 117.1 142.4 150.9 128.5 427 6 102.8 112.0 135.0 135.0 145.8 126.1 43.0 7 120.4 84.3 12.8 118.5 119.3 O 361 8 1327 13 124.0 123.9 105. 1274 460 9 136.4 126.2 154.7 127.1 173.2 143.5 469 135.0 115.4 1491 1383 130.4 133.6 337 11 139.6 127.9 5. 143.7 10.5 134.6 406 125.3 160.2 1304 1324 165.1 146.7 398 13 145.7 0.8 49.5 3.3 151.8 1324 500 138.6 139.0 1319 1402 141.1 138.1 9.2 15 10 114.6 165. 113.8 139.6 128.7 54.8 145.2 101.0 154.6 120.2 117.3 1276 533 17 125.9 135.3 215 1479 05.0 127.1 429 18 129.7 973 130.5 109.0 150.5 1234 532 19 23.4 150,0 616 1484 154.2 147.5 383 20 144.8 138.3 119.6 1518 142.7 1394 32.2 10 12 14 16 TABLE 6E. 10 Additional Data for Exercise 6.20, part (b) Sample Number rsR 131.0 184.8 182.3 143.3 212.8 1708 SLS 2 1813 193.2 180.7 169.1 174.3 179.7 24.0 3 154.8 17υ,2 168.4 202.7174.4 174.148.0 4 1575 1542 1691 142.2 161.9 157.0 269 5 2163 174.3 1662 155.5 184.3 179.3 608 1869 180.2 1492 175.2 185.0 1753 378 7 1678 143.9 157.5 171.8 194.9 167.2 51.0 8 178.2 186.7 1424 1594 1676 166.9 44.2 9 162.6 143.6 132.8 168.9 177.2 157.0 44.5 10 172.1 191. 203.4 150.4 196.3 1828 53.0 s TABLE 6E.11 New Data for Exercise 6.20, part c Sample Number R 131.5 143.1 118.5 103.2 121.6 123.6 39.8 111.0 127.3 110.4 910 143.9 116.7 528 129.8 98.3 134.0 105.1 133. 120. 35.7 145.2 132.8 106.1 131.0 992 1228 46.0 114.6 111.0 108.8 177ฐ 121.6 126.7 687 6 125.2 864 64.4 137.1 1175 1061 726 7 145.9 109.5 84.9 129.8 10.6 16.1 61.0 8 123.6 114.0 135.4 832 107.6 1128 522 85.8 156.3 9. 962 153.0 122.2 706 10 107.4 148.7 1274 1250 127.5 127.2 413