Hint: Lots of numbers to “crunch” here – be careful! If you’d like, use EXCEL to
ID: 361469 • Letter: H
Question
Hint: Lots of numbers to “crunch” here – be careful! If you’d like, use EXCEL to make the calculations easier. You can copy and paste the table to excel.
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
a. Determine X=X and RR . (Do not round intermediate calculations. Round your answers to 3 decimal places.)
b. Determine the UCL and LCL for a %media:formula252.mml%-chart. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
c. 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.)
d. What comments can you make about the process?
The process is out of statistical control.
The process is in statistical control.
OBSERVATIONS
SAMPLE NUMBER 1 2 3 4 5 1 0.480 0.497 0.489 0.515 0.482 2 0.479 0.496 0.513 0.488 0.526 3 0.504 0.496 0.506 0.479 0.518 4 0.503 0.496 0.476 0.478 0.481 5 0.481 0.502 0.519 0.453 0.484 6 0.481 0.496 0.497 0.495 0.501 7 0.503 0.513 0.490 0.475 0.512 8 0.512 0.541 0.492 0.476 0.491 9 0.495 0.541 0.508 0.499 0.512 10 0.505 0.497 0.513 0.515 0.489 11 0.504 0.476 0.452 0.498 0.491 12 0.461 0.467 0.529 0.499 0.517 13 0.513 0.513 0.495 0.518 0.511 14 0.495 0.518 0.497 0.499 0.505 15 0.502 0.513 0.491 0.515 0.512 16 0.479 0.496 0.413 0.471 0.529 17 0.464 0.475 0.412 0.481 0.488 18 0.501 0.489 0.352 0.482 0.475 19 0.500 0.526 0.478 0.489 0.497 20 0.485 0.490 0.326 0.499 0.513Explanation / Answer
Following table presents the values for each sample from which Mean as well as Range for data against each sample have been calculated and presented
It is to be noted that :
Mean for any sample number = Sum of 5 observations / 5
Range for any sample number = Highest value – Lowest value in that sample
Total for Mean = Sum of all mean values ( total 20 sets of data)
Total for Range = Sum of all range values ( total 20 sets of data )
O B S E R V A T I O N ------------------------------>>>>
Sample Number
1
2
3
4
5
Mean
Range
1
0.48
0.497
0.489
0.515
0.482
0.4926
0.035
2
0.479
0.496
0.513
0.488
0.526
0.5004
0.047
3
0.504
0.496
0.506
0.479
0.518
0.5006
0.039
4
0.503
0.496
0.476
0.478
0.481
0.4868
0.027
5
0.481
0.502
0.519
0.453
0.484
0.4878
0.066
6
0.481
0.496
0.497
0.495
0.501
0.494
0.02
7
0.503
0.513
0.49
0.475
0.512
0.4986
0.038
8
0.512
0.541
0.492
0.476
0.491
0.5024
0.065
9
0.495
0.541
0.508
0.499
0.512
0.511
0.046
10
0.505
0.497
0.513
0.515
0.489
0.5038
0.026
11
0.504
0.476
0.452
0.498
0.491
0.4842
0.052
12
0.461
0.467
0.529
0.499
0.516
0.4944
0.068
13
0.513
0.513
0.495
0.518
0.511
0.51
0.023
14
0.495
0.518
0.497
0.499
0.505
0.5028
0.023
15
0.502
0.513
0.491
0.515
0.512
0.5066
0.024
16
0.479
0.496
0.413
0.471
0.529
0.4776
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
0.4598
0.149
19
0.5
0.526
0.478
0.489
0.497
0.498
0.048
20
0.485
0.49
0.326
0.499
0.513
0.4626
0.187
TOTAL:
9.838
1.175
Thus,
Xbar-bar
= Sum of mean values/ Number of observations
= 9.838/ 20
= 0.4919
Rbar
= Sum of Range values / Number of observations
= 1.175/20
= 0.05875
Given ,
Sample size = n = 5
The Relevant values of constants as derived from standard table of constants for Xbar and R charts as follows :
A2 = 0.577
D4 = 2.114
D3 = 0
Control Charts for Xbar chart :
Upper Control Limit = UCL
= Xbr-bar + A2.Rbar
= 0.4919 + 0.577 x 0.05875
= 0.4919 + 0.0339
= 0.5258
Lower Control Limit = LCL
= Xbr-bar - A2.Rbar
= 0.4919 - 0.577 x 0.05875
= 0.4919 - 0.0339
= 0.458
Control Chart for R chart :
Upper Control Limit = UCL = D4.Rbar = 2.114 x 0.05875 = 0.1242
Lower Control Limit = LCL = 0
O B S E R V A T I O N ------------------------------>>>>
Sample Number
1
2
3
4
5
Mean
Range
1
0.48
0.497
0.489
0.515
0.482
0.4926
0.035
2
0.479
0.496
0.513
0.488
0.526
0.5004
0.047
3
0.504
0.496
0.506
0.479
0.518
0.5006
0.039
4
0.503
0.496
0.476
0.478
0.481
0.4868
0.027
5
0.481
0.502
0.519
0.453
0.484
0.4878
0.066
6
0.481
0.496
0.497
0.495
0.501
0.494
0.02
7
0.503
0.513
0.49
0.475
0.512
0.4986
0.038
8
0.512
0.541
0.492
0.476
0.491
0.5024
0.065
9
0.495
0.541
0.508
0.499
0.512
0.511
0.046
10
0.505
0.497
0.513
0.515
0.489
0.5038
0.026
11
0.504
0.476
0.452
0.498
0.491
0.4842
0.052
12
0.461
0.467
0.529
0.499
0.516
0.4944
0.068
13
0.513
0.513
0.495
0.518
0.511
0.51
0.023
14
0.495
0.518
0.497
0.499
0.505
0.5028
0.023
15
0.502
0.513
0.491
0.515
0.512
0.5066
0.024
16
0.479
0.496
0.413
0.471
0.529
0.4776
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
0.4598
0.149
19
0.5
0.526
0.478
0.489
0.497
0.498
0.048
20
0.485
0.49
0.326
0.499
0.513
0.4626
0.187
TOTAL:
9.838
1.175
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