Eight oven burners are configured to provide controlled heating for metal casing configurations in an annealing process. The burner temperatures are denoted t1, t2, …, t8 in the following table. (a) Create a matrix plot and comment on any observed correlations. (b) Perform principal components analysis selecting the correlation option and select the principal components that explain at least 90% of the variation. Create a matrix plot of these principal component scores and comment on any remaining observed correlations. (c) Create an Individuals control chart for each standardized principal component scores from part (b) and determine whether all casing batches were processed in a state of control.
Batch t1 t2 t3. t4 t5 t6 t7 t8
1. 507 516 527 516 499. 512 472 477
2 512 513 533 518 502. 510 476. 475
3. 520 512 537 518 503 512 480 477
4. 520 514 538 516 504. 517 480 479
5 530 515. 542. 525 504 512. 481 477
6 528 516. 541. 524 505. 514 482 480
7 522 513 537. 518 503 512 479 477
8 527 509. 537 521. 504 508 478 472
9 533 514. 528 529. 508 512 482 477
10 530. 512. 538 524. 507 512. 482 477
11 530 512 541 525 507 511 482 476
12 527. 513 541 523 506 512 481 476
13 529 514 542 525 506 512 481 477
14. 522 509 539. 518 501 510 476 475
15 532 515 545 528 507 511 481 478
16 531 514 543. 525 507 511. 482 477
17 535 514 542 530. 509 511. 483 477
18 516. 515 537 515 501 516 476. 481
19 514 510. 532 512 497 512 471 476
20 536 512. 540. 526. 509 512 482 477
21. 522 514 540 518. 497. 514 475 478
22 520 514 540 518 501 514 475 478
23 526 517 546 522 502 516 477 480
24 527 514 543 523 502 512 475 476
25 529 518. 544 525 504 516 479 481
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