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In: Statistics and Probability

Rosters Chicken advertises “lite” chicken with 30% fewer calories than standard chicken. Rosters wants to use...

Rosters Chicken advertises “lite” chicken with 30% fewer calories than standard chicken. Rosters wants to use control charts to monitor the calories in its chicken.  To do this it periodically takes a sample of 5 chicken breasts off its production line and measures the caloric content of each chicken.  This data is shown for 15 samples in the tab Chicken of the Excel data file HW5_Data.xlsx.  

  1. Calculate 3-sigma control limits for the caloric content of chicken breasts produced by this process, for both the means and the range charts.
  2. Plot the means and ranges on their respective charts.  Can you conclude that the process is in control?
  3. Would you use the control limits in (a) for real-time monitoring of the process?  Explain.
  4. Ten more samples are shown on tab Chicken-2.  Plot these sample means and ranges against the control limits of (a).  What can you conclude about the process?
    Chicken
    Sample # Obs-1 Obs-2 Obs-3 Obs-4 Obs-5
    1 448 391 465 443 429
    2 373 437 412 432 421
    3 455 416 429 439 408
    4 434 380 444 390 396
    5 461 431 414 411 439
    6 454 451 410 421 471
    7 410 417 393 392 419
    8 445 438 396 438 418
    9 394 433 461 374 378
    10 385 408 442 445 421
    11 409 422 376 441 468
    12 430 446 435 422 414
    13 413 394 383 404 439
    14 474 450 447 411 432
    15 435 476 417 443 473
    Chicken 2
    Sample # Obs-1 Obs-2 Obs-3 Obs-4 Obs-5
    1 403 426 481 432 476
    2 475 467 387 430 447
    3 392 405 438 405 409
    4 393 446 395 438 427
    5 402 460 405 403 395
    6 456 472 423 456 381
    7 403 442 429 517 437
    8 472 450 438 438 414
    9 381 449 478 409 454
    10 423 401 487 421 422

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