The following table contains the measurements of the key length dimension from a

Question

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. Refer Exhibit 10.13 OBSERVATIONS SAMPLE NUMBER 2 0.482 0.503 0.485 0.503 0.499 0.484 0.507 0.492 0.485 0.482 0.461 0.483 0.471 0.472 0.506 0.507 0.482 0.506 0.524 0.483 0.485 0.498 0.495 0.494 0.471 0.472 0.498 0.522 0.493 0.494 0.495 0.479 0.451 0.521 0.486 0.523 0.521 0.483 0.487 0.496 0.506 0.495 0.512 0.493 0.488 0.523 0.511 2 3 0.512 0.483 0.525 0.504 0.482 0.492 0.517 5 6 0.498 0.503 0.504 0.483 0.462 0.483 0.484 0.524 0.5040.507 0.501 0.493 0.472 0.504 0.483 0.482 0.473 0.507 0.483 0.485 0.486 0.493 0.506 0.493 0.474 0.464 0.503 0.485 0.483 0.527 0.482 0.512 0.517 0.492 0.472 0.482 0.512 0.509 a. Calculate the mean and range for the above samples. (Do not round intermediate calculations Round your answers to 3 decimal places.) Sample Number Mean Range 3

Explanation / Answer

SAMPLE NUMBER 1     2     3    4     5     Mean (x bar) Range R 1              0.485 0.482 0.483 0.507 0.486 0.4886 0.025 2              0.498 0.503 0.519 0.492 0.523 0.507 0.031 3              0.495 0.485 0.512 0.485 0.521 0.4996 0.036 4              0.494 0.503 0.483 0.482 0.483 0.489 0.021 5              0.471 0.499 0.525 0.461 0.487 0.4886 0.064 6              0.472 0.484 0.504 0.483 0.496 0.4878 0.032 7              0.498 0.513 0.482 0.471 0.506 0.494 0.042 8              0.522 0.498 0.492 0.472 0.495 0.4958 0.05 9              0.493 0.503 0.517 0.506 0.512 0.5062 0.024 10              0.494 0.504 0.519 0.507 0.493 0.5034 0.026 11              0.495 0.483 0.462 0.482 0.488 0.482 0.033 12              0.479 0.451 0.513 0.506 0.523 0.4944 0.072 13              0.521 0.513 0.483 0.524 0.511 0.5104 0.041 14              0.484 0.524 0.504 0.507 0.501 0.504 0.04 15              0.493 0.519 0.493 0.507 0.512 0.5048 0.026 16              0.474 0.503 0.472 0.483 0.517 0.4898 0.045 17              0.464 0.485 0.504 0.485 0.492 0.486 0.04 18              0.518 0.483 0.483 0.486 0.472 0.4884 0.046 19              0.512 0.527 0.482 0.493 0.482 0.4992 0.045 20              0.509 0.482 0.473 0.506 0.512 0.4964 0.039 Mean 0.49355 0.4972 0.49525 0.49225 0.5006 0.49577 0.0389 X double bar R bar standerd Deviation 0.00819326 From the Table of Constants for Control charts X bar n 5 UCL X Double bar +A2 *R bar 0.5182153 A2 0.577 LCL X Double bar - A2 *R bar 0.4733247 D3 0 D4 2.114 R bar UCL D4 * R bar 0.0822346 LCL D3 * R bar 0

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