# solution

The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one-hour intervals. Use three-sigma control limits. Use Exhibit 10.13.

 OBSERVATIONS SAMPLE NUMBER 1 2 3 4 5 1 0.487 0.481 0.485 0.509 0.484 2 0.501 0.505 0.517 0.490 0.525 3 0.497 0.499 0.514 0.486 0.516 4 0.496 0.505 0.485 0.483 0.488 5 0.473 0.503 0.523 0.468 0.487 6 0.474 0.483 0.506 0.481 0.504 7 0.496 0.511 0.493 0.472 0.497 8 0.523 0.505 0.494 0.473 0.493 9 0.495 0.500 0.513 0.502 0.501 10 0.494 0.501 0.517 0.509 0.491 11 0.496 0.485 0.460 0.492 0.486 12 0.484 0.460 0.511 0.497 0.515 13 0.525 0.511 0.481 0.526 0.513 14 0.488 0.522 0.506 0.507 0.503 15 0.491 0.517 0.498 0.509 0.509 16 0.472 0.505 0.470 0.481 0.528 17 0.469 0.482 0.512 0.483 0.497 18 0.516 0.485 0.481 0.484 0.470 19 0.512 0.525 0.483 0.491 0.495 20 0.498 0.493 0.471 0.497 0.511

a.Calculate the mean and range for the above samples.(Do not round intermediate calculations. Round your answers to 3 decimal places.)

b.Determine X=X= and R-R- . (Do not round intermediate calculations. Round your answers to 3 decimal places.)

c.Determine the UCL and LCL for a X-X- -chart. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

d.Determine the UCL and LCL for R-chart.