Question
In: Mechanical Engineering
The net weight (in oz.) of a dry bleach product is to be monitored by X...
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The net weight (in oz.) of a dry bleach product is to be monitored by X and R and X and S control charts using a sample size of n = 5. Data for 20 preliminary samples are shown below.
|
Subgroup Number |
X1 |
X2 |
X3 |
X4 |
X5 |
For X and R UCLX=X̿+A2R CLX=X̿=i=1gXig LCLX=X̿-A2R UCLR=D4R CLR=R =i=1gRig LCLR=D3R For X and S. UCLX=X̿+A3S CLX=X̿=i=1gXig LCLX=X̿-A3S UCLS=B4S CLS=S =i=1gSig LCLS=B3S |
|
|
1 |
12 |
9 |
13 |
15 |
12 |
||
|
2 |
10 |
7 |
16 |
14 |
8 |
||
|
3 |
7 |
8 |
10 |
6 |
9 |
||
|
4 |
8 |
9 |
15 |
13 |
7 |
||
|
5 |
9 |
10 |
7 |
13 |
16 |
||
|
6 |
12 |
11 |
10 |
10 |
8 |
||
|
7 |
16 |
10 |
14 |
9 |
12 |
||
|
8 |
17 |
8 |
10 |
14 |
13 |
||
|
9 |
9 |
10 |
8 |
12 |
10 |
||
|
10 |
15 |
16 |
10 |
13 |
12 |
||
|
11 |
8 |
12 |
14 |
16 |
11 |
||
|
12 |
16 |
13 |
9 |
11 |
8 |
||
|
13 |
16 |
11 |
13 |
15 |
10 |
||
|
14 |
15 |
13 |
10 |
12 |
9 |
||
|
15 |
11 |
9 |
8 |
16 |
11 |
||
|
16 |
15 |
13 |
11 |
14 |
12 |
||
|
17 |
9 |
11 |
12 |
10 |
14 |
||
|
18 |
15 |
12 |
10 |
11 |
13 |
||
|
19 |
8 |
6 |
9 |
12 |
10 |
||
|
20 |
13 |
8 |
11 |
15 |
9 |
||
Determine the trial central line and control limits for the X and R (24 points).
UCLX=
CLX=
LCLX=
UCLR=
CLR=
LCLR=
Determine the trial central line and control limits for the X and S (24 points).
UCLX=
CLX=
LCLX=
UCLS=
CLS=
LCLS=
Solutions
Expert Solution
Calculation
| Measured values | |||||||||
| Sample | X1 | X2 | X3 | X4 | X5 |
Sample Average X bar |
Range ( max-min) |
(x-xbar)^2 | Sub group SD |
| 1 | 12 | 9 | 13 | 15 | 12 | 12.20 | 4 | 0.7744 | 2.17 |
| 2 | 10 | 7 | 16 | 14 | 8 | 11.00 | 9 | 0.1024 | 3.87 |
| 3 | 7 | 8 | 10 | 6 | 9 | 8.00 | 3 | 11.0224 | 1.58 |
| 4 | 8 | 9 | 15 | 13 | 7 | 10.40 | 7 | 0.8464 | 3.44 |
| 5 | 9 | 10 | 7 | 13 | 16 | 11.00 | 3 | 0.1024 | 3.54 |
| 6 | 12 | 11 | 10 | 10 | 8 | 10.20 | 2 | 1.2544 | 1.48 |
| 7 | 16 | 10 | 14 | 9 | 12 | 12.20 | 6 | 0.7744 | 2.86 |
| 8 | 17 | 8 | 10 | 14 | 13 | 12.40 | 9 | 1.1664 | 3.51 |
| 9 | 9 | 10 | 8 | 12 | 10 | 9.80 | 2 | 2.3104 | 1.48 |
| 10 | 15 | 16 | 10 | 13 | 12 | 13.20 | 6 | 3.5344 | 2.39 |
| 11 | 8 | 12 | 14 | 16 | 11 | 12.20 | 6 | 0.7744 | 3.03 |
| 12 | 16 | 13 | 9 | 11 | 8 | 11.40 | 7 | 0.0064 | 3.21 |
| 13 | 16 | 11 | 13 | 15 | 10 | 13.00 | 5 | 2.8224 | 2.55 |
| 14 | 15 | 13 | 10 | 12 | 9 | 11.80 | 5 | 0.2304 | 2.39 |
| 15 | 11 | 9 | 8 | 16 | 11 | 11.00 | 3 | 0.1024 | 3.08 |
| 16 | 15 | 13 | 11 | 14 | 12 | 13.00 | 4 | 2.8224 | 1.58 |
| 17 | 9 | 11 | 12 | 10 | 14 | 11.20 | 3 | 0.0144 | 1.92 |
| 18 | 15 | 12 | 10 | 11 | 13 | 12.20 | 5 | 0.7744 | 1.92 |
| 19 | 8 | 6 | 9 | 12 | 10 | 9.00 | 3 | 5.3824 | 2.24 |
| 20 | 13 | 8 | 11 | 15 | 9 | 11.20 | 5 | 0.0144 | 2.86 |
| Total | 226.40 | 97 | |||||||
| Average X bar | 11.32 | ||||||||
| R bar | 4.85 | ||||||||
| Σ(x-xbar)^2 | 34.832 | ||||||||
| Σ(x-xbar)^2 / n-1 | 1.35 | ||||||||
| SD | 1.35 | ||||||||
| Sample SD Average Sbar | 2.56 | ||||||||
| X bar USL | Xbar + A2*R | A2 =0.577 |
 samet mamat answered 3 months agoRelated SolutionsThe net weight (in oz.) of a dry bleach product is to be monitored by X...
The net weight (in oz.) of a dry bleach product is to be
monitored by X and R and X and S control charts
using a sample size of n = 5. Data for 20 preliminary samples are
shown below.
Subgroup Number
X1
X2
X3
X4
X5
1
12
10
13
15
12
2
10
7
16
14
8
3
11
12
10
16
9
4
8
9
15
13
7
5
9
10
14
13
16
6
12
11...
The net weight (in oz.) of a dry bleach product is to be monitored by X...The net weight (in oz.) of a dry bleach product is to be
monitored by X ̅ and R and X ̅ and S control charts using a sample
size of n = 5. Data for 20 preliminary samples are shown below.
Subgroup Number
X1
X2
X3
X4
X5
1
8
10
11
15
12
2
10
9
16
14
8
3
11
12
10
16
14
4
7
11
8
13
9
5
9
10
12
11
16
6...
The net weight (in oz.) of a dry bleach product is to be monitored by X...
The net weight (in oz.) of a dry bleach product is to be
monitored by X and R and X and S control charts
using a sample size of n = 5. Data for 20 preliminary samples are
shown below.
Subgroup Number
X1
X2
X3
X4
X5
1
12
10
13
15
12
2
10
7
16
14
8
3
11
12
10
16
14
4
8
11
15
13
7
5
9
10
14
13
16
6
12
11...
The net weight (in oz.) of a dry bleach product is to be monitored by and R and and...
The net weight (in oz.) of a dry bleach product is to be
monitored by and R and and
S control charts using a sample size of n = 5. Data for
20 preliminary samples are shown below.
Subgroup Number
X1
X2
X3
X4
X5
1
12
9
13
15
12
2
10
7
16
14
8
3
7
8
10
6
9
4
8
9
15
13
7
5
9
10
7
13
16
6
12
11
10
10
8
7
16
10...
The net weight (in oz.) of a dry bleach product is to be monitored by and R and and...
The net weight (in oz.) of a dry bleach product is to be
monitored by and R and and
S control charts using a sample size of n = 5. Data for
20 preliminary samples are shown below.
Subgroup Number
X1
X2
X3
X4
X5
1
12
9
13
15
12
2
10
7
16
14
8
3
7
8
10
6
9
4
8
9
15
13
7
5
9
10
7
13
16
6
12
11
10
10
8
7
16
10...
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