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Constructing a three-sigma x chart and r chart


Problem: 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.
OBSERVATIONS
SAMPLE





 NUMBER
1 2 3 4 5
1
0.486 0.499 0.493 0.511 0.481
2
0.499 0.506 0.516 0.494 0.529
3
0.496 0.500 0.515 0.488 0.521
4
0.495 0.506 0.483 0.487 0.489
5
0.472 0.502 0.526 0.469 0.481
6
0.473 0.495 0.507 0.493 0.506
7
0.495 0.512 0.490 0.471 0.504
8
0.525 0.501 0.498 0.474 0.485
9
0.497 0.501 0.517 0.506 0.516
10
 0.495  0.505 0.516  0.511 0.497
11
 0.495  0.482 0.468  0.492 0.492
12
 0.483  0.459 0.526  0.506 0.522
13
 0.521  0.512 0.493  0.525 0.510
14
 0.487  0.521 0.507  0.501 0.500
15
 0.493  0.516 0.499  0.511 0.513
16
 0.473  0.506 0.479  0.480 0.523
17
 0.477  0.485 0.513  0.484 0.496
18
 0.515  0.493 0.493  0.485 0.475
19
 0.511  0.536 0.486  0.497 0.491
20
 0.509  0.490 0.470  0.504 0.512

Construct a three-sigma X chart and R chart (use Exhibit) for the length of the fuel injector.                           

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