In: Advanced Math
Problem 10-29 (Algo)
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 |
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SAMPLE NUMBER | 1 | 2 | 3 | 4 | 5 |
1 | 0.481 | 0.486 | 0.492 | 0.517 | 0.475 |
2 | 0.485 | 0.505 | 0.527 | 0.491 | 0.528 |
3 | 0.486 | 0.487 | 0.513 | 0.487 | 0.524 |
4 | 0.481 | 0.505 | 0.468 | 0.486 | 0.486 |
5 | 0.467 | 0.503 | 0.512 | 0.468 | 0.479 |
6 | 0.468 | 0.493 | 0.502 | 0.491 | 0.508 |
7 | 0.485 | 0.507 | 0.486 | 0.479 | 0.507 |
8 | 0.532 | 0.504 | 0.485 | 0.480 | 0.483 |
9 | 0.493 | 0.505 | 0.515 | 0.507 | 0.499 |
10 | 0.492 | 0.507 | 0.509 | 0.517 | 0.481 |
11 | 0.491 | 0.512 | 0.469 | 0.490 | 0.496 |
12 | 0.484 | 0.441 | 0.521 | 0.507 | 0.525 |
13 | 0.529 | 0.495 | 0.491 | 0.518 | 0.507 |
14 | 0.482 | 0.497 | 0.507 | 0.491 | 0.503 |
15 | 0.492 | 0.511 | 0.483 | 0.517 | 0.506 |
16 | 0.461 | 0.502 | 0.480 | 0.478 | 0.525 |
17 | 0.471 | 0.474 | 0.514 | 0.477 | 0.491 |
18 | 0.521 | 0.512 | 0.491 | 0.475 | 0.480 |
19 | 0.505 | 0.552 | 0.486 | 0.481 | 0.489 |
20 | 0.502 | 0.482 | 0.481 | 0.507 | 0.507 |
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. (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Round your answers to 3 decimal places.)
e. What comments can you make about the process?
Process is in statistical control.
Process is out of statistical control.