1 answer

Problem 10-29 (Algo) The following table contains the measurements of the key length dimension from a...

Question:

Problem 10-29 (Algo) The following table contains the measurements of the key length dimension from a fuel injector. These saa. Calculate the mean and range for the above samples. (Do not round intermediate calculations. Round your answers to 3 decimb. Determine X and R. (Do not round intermediate calculations. Round your answers to 3 decimal places.) X bar R bar c. Determd. Determine the UCL and LCL for R-chart. (Leave no cells blank - be certain to enter O wherever required. Do not round int

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. SAMPLE NUMBER WNEOVO UN 1 0.480 0.479 0.504 0.503 0.481 0.481 0.503 0.512 0.495 0.505 0.504 0.461 0.513 0.495 0.502 0.479 0.464 0.501 0.500 0.485 OBSERVATIONS 2 3 4 5 0.497 0.489 0.515 0.482 0.496 0.513 0.488 0.526 0.496 0.506 0.4790.518 0.496 0.476 0.478 0.481 0.502 0.519 0.453 0.484 0.496 0.497 0.495 0.501 0.513 0.490 0.475 0.512 0.541 0.492 0.476 0.491 0.541 0.508 0.499 0.512 0.497 0.513 0.515 0.489 0.476 0.4520.498 0.491 0.467 0.529 0.499 0.517 0.513 0.495 0.518 0.511 0.518 0.497 0.499 0.505 0.513 0.491 0.515 0.512 0.496 0.413 0.471 0.529 0.475 0.412 0.481 0.488 0.489 0.352 0.482 0.475 0.526 0.478 0.489 0.497 0.490 0.326 0.499 0.513 O
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
b. Determine X and R. (Do not round intermediate calculations. Round your answers to 3 decimal places.) X bar R bar c. Determine the UCL and LCL for a X-chart. (Do not round intermediate calculations. Round your answers to 3 decimal places.) UCL LCL
d. Determine the UCL and LCL for R-chart. (Leave no cells blank - be certain to enter "O" wherever required. Do not round intermediate calculations. Round your answers to 3 decimal places.) UCL LCL e. What comments can you make about the process? O Process is in statistical control. O Process is out of statistical control.

Answers

Note: Answers (in decimals) depend on table 10.13 which you have not posted. We have taken the values of A2 and D4 from similar tables from the book.

Sample Obs-1 Obs-2 Obs-3 Obs-4 Obs-5 X-bar Range n 5
1 0.480 0.497 0.489 0.515 0.482 0.493 0.035 A2 0.58
2 0.479 0.496 0.513 0.488 0.526 0.500 0.047 D3 0
3 0.504 0.496 0.506 0.479 0.518 0.501 0.039 D4 2.11
4 0.503 0.496 0.476 0.478 0.481 0.487 0.027
5 0.481 0.502 0.519 0.453 0.484 0.488 0.066 UCLX 0.526
6 0.481 0.496 0.497 0.495 0.501 0.494 0.020 LCLX 0.458
7 0.503 0.513 0.490 0.475 0.512 0.499 0.038
8 0.512 0.541 0.492 0.476 0.491 0.502 0.065 LCLR 0
9 0.495 0.541 0.508 0.499 0.512 0.511 0.046 UCLR 0.124
10 0.505 0.497 0.513 0.515 0.489 0.504 0.026
11 0.504 0.476 0.452 0.498 0.491 0.484 0.052
12 0.461 0.467 0.529 0.499 0.517 0.495 0.068
13 0.513 0.513 0.495 0.518 0.511 0.510 0.023
14 0.495 0.518 0.497 0.499 0.505 0.503 0.023
15 0.502 0.513 0.491 0.515 0.512 0.507 0.024
16 0.479 0.496 0.413 0.471 0.529 0.478 0.116
17 0.464 0.475 0.412 0.481 0.488 0.464 0.076
18 0.501 0.489 0.352 0.482 0.475 0.460 0.149
19 0.500 0.526 0.478 0.489 0.497 0.498 0.048
20 0.485 0.490 0.326 0.499 0.513 0.463 0.187
Avg. 0.492 0.059
X_double-bar R-bar

Calculations:

K A 1 Sample 21 J n Az D: D. NM 5 0.58 0 2.11 5 6 4 5 UCLX =G22+K2*H22 LCLX =G22-K2*H22 98 UCL =K3*H22 LCLR =K4*H22 10 9 11 1

(a)

Sample Mean Range
1 0.493 0.035
2 0.500 0.047
3 0.501 0.039
4 0.487 0.027
5 0.488 0.066
6 0.494 0.020
7 0.499 0.038
8 0.502 0.065
9 0.511 0.046
10 0.504 0.026
11 0.484 0.052
12 0.495 0.068
13 0.510 0.023
14 0.503 0.023
15 0.507 0.024
16 0.478 0.116
17 0.464 0.076
18 0.460 0.149
19 0.498 0.048
20 0.463 0.187

(b)

X_double-bar 0.492
R-bar 0.059

(c)

UCLX 0.526
LCLX 0.458

(d)

UCLR 0.124
LCLR 0

(e)

Out of control as the sample ranges for samples 18 and 20 are more than UCL.

.

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