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 ta 516 ts 499 to 512 477 1 507 516 527 472 476 513 512 514 2 512 533 518 502 510 475 3 537 518 320 520 530 528 522 527 503 504 504 505 503 512 517 480 477 538 516 480 479 5 515 542 525 512 481 477 516 513 509 6 541 537 537 524 514 482 480 7 518 512 479 477 521 504 508 478 472 533 514 512 528 529 5os 512 482 477 10 530 538 524 507 512 511 482 477 11 530 512 541 525 507 482 476 476 477 475 478 12 527 529 513 541 523 506 512 481 13 514 542 525 506 512 481 476 481 14 522 509 539 518 501 510 15 532 515 545 528 507 511 16 531 514 543 525 507 511 482 477 17 535 514 542 530 509 501 497 511 483 477 18 516 515 537 515 516 476 481 514 536 10 512 532 540 512 526 512 512 471 482 476 477 19 20 21 22 509 522 514 540 518 497 514 475 478 520 514 517 514 540 518 501 514 475 478 23 526 546 522 502 516 477 480 24 527 543 523 502 512 475 476 25 529 518 544 525 504 516 479 481