A process considered to be in control measures an ingredient in ounces. Roberto Baggio, a quality inspector took 20 samples, each with 8 observations as follows: thats in the pictuer after that using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation of the process is 0.693. First: perform all actions and calculations needed to answer the question. All equations/calculations needed to be fully written STEP by STEP. No short calculations or direct answers/results will be accepted. This applies to the calculations for both types of control limits (mean and range). Second: Explain the process followed to identify each type of control limit and any observations made in the problem-solving process.

Practical Management Science
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A process considered to be in control measures an ingredient in ounces.                                                                                        

Roberto Baggio, a quality inspector took 20 samples, each with 8 observations as follows:

thats in the pictuer

after that using this information, obtain three-sigma (i.e., z=3) control limits for a mean control chart and control limits for a range chart, respectively. It is known from previous experience that the standard deviation of the process is 0.693.

First: perform all actions and calculations needed to answer the question. 

All equations/calculations needed to be fully written STEP by STEP.  No short calculations or direct answers/results will be accepted.

This applies to the calculations for both types of control limits (mean and range). 

 

Second: Explain the process followed to identify each type of control limit and any observations made in the problem-solving process. 

 

thank you very much

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Transcribed Image Text:SAMPLES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 17 18 19 20 1 11 7 13 9 12 11 13 10 8 10 11 12 13 9 8 9 11 12 9 11 2 9 8 o 9 10 10 10 12 10 8 12 9 11 9 8 10 10 10 10 12 11 OBSERVATIONS 3 10 12 10 8 9 8 10 8 12 11 10 11 10 11 9 8 9 11 12 9 4 13 9 ∞56 12 8 7 9 11 9 11 10 12 11 12 12 14 11 12 9 12 10 5 10 6 12 11 9 10 14 10 13 11 11 12 11 9 13 15 15 11 11 10 LO 6 11 8 11 12 12 14 15 11 10 12 13 10 12 11 13 16 14 12 13 11 11 7 9 11 10 10 11 12 8 10 12 10 9 10 10 11 12 8 9 12 8 8 12 10 9 10 8 aa 9 9 9 10 12 12 13 9 10 12 Ñ 9 10 10 9 12
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thank you for your answer i found something similar on bertleby but the working out is different and the answers are slighilty different too i am not sure which one to use:

this is the answer that i found:

this are his answers but in the picture is working out

X chart values

UCL 11.30

CL 10.57

LCL 9.83

R chart values

UCL 3.67

LCL 0.27

A
1
2 Samples
31
4 2
5 3
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9 7
10 8
11 9
12 10
13 11
14 12
15 13
16 14
17 15
18 15
19 17
20 18
21 19
22 20
23
24
25
B C D E F G
Observations
2 3
1
11 9
7
13 9
10 12
9 108
8
12 10 9 7
11 10 8
9
13 12 10 11
10 10 8 9
8 8 12 11
10 12 11
119
4 5 6 7
8
10 13 10 11 9 12
6 8 11 10
12 11 10 9
11 12 10 10
9 12 11 8
10 14 129
15 8 9
14
10
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11 12 10 12
10
10 12 11 13 9 12
12 11
11 11 12
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13 9
10 12 11
12 10 9
9
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8
10 9
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13 11 12
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10 8
11 15
16 12 9
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12 15 14 8
11
12 10 11 9
12 9
13 12
9 12 12 12 11
9
11 11 9 10 10 11 8 12
H
8 12 9
-
10
oo
10
x bar
J
10.63
8.88
10.75
9.75
9.75
10.38
11.50
9.63
10.50
11.00
10.88
11.38
10.75
10.00
11.25
11.25
11.13
10.50
11.25
10.25
10.57
x double bar
K
Here,
sample size (number of observations), n
Z is given
sigma (standard deviation), o
From control chart table
D3
D4
A2
X chart values
UCL
CL
LCL
R chart values
UCL
LCL
M
8
3
0.693
0.136
1.864
0.373
11.30
10.57
9.83
3.67
0.27
Transcribed Image Text:A 1 2 Samples 31 4 2 5 3 6 4 7 5 8 6 9 7 10 8 11 9 12 10 13 11 14 12 15 13 16 14 17 15 18 15 19 17 20 18 21 19 22 20 23 24 25 B C D E F G Observations 2 3 1 11 9 7 13 9 10 12 9 108 8 12 10 9 7 11 10 8 9 13 12 10 11 10 10 8 9 8 8 12 11 10 12 11 119 4 5 6 7 8 10 13 10 11 9 12 6 8 11 10 12 11 10 9 11 12 10 10 9 12 11 8 10 14 129 15 8 9 14 10 11 10 9 13 10 12 10 11 12 10 12 10 10 12 11 13 9 12 12 11 11 11 12 10 11 13 13 9 10 12 11 12 10 9 9 8 11 12 9 11 10 10 8 10 9 14 13 13 11 12 9 10 8 11 15 16 12 9 11 10 9 12 15 14 8 11 12 10 11 9 12 9 13 12 9 12 12 12 11 9 11 11 9 10 10 11 8 12 H 8 12 9 - 10 oo 10 x bar J 10.63 8.88 10.75 9.75 9.75 10.38 11.50 9.63 10.50 11.00 10.88 11.38 10.75 10.00 11.25 11.25 11.13 10.50 11.25 10.25 10.57 x double bar K Here, sample size (number of observations), n Z is given sigma (standard deviation), o From control chart table D3 D4 A2 X chart values UCL CL LCL R chart values UCL LCL M 8 3 0.693 0.136 1.864 0.373 11.30 10.57 9.83 3.67 0.27
X bar chart formula when Standard deviation is known
Upper control limit (UCL):
Lower control limit (LCL):
where
OF
σ =
=
= σ/√n
Standard deviation of distribution of sample means
LCL =
x+205
ZO
= x
o = Estimate of the process standard deviation
n = Sample size
z = Standard normal deviate
x = Average of sample means
3D30
42 √n
R bar chart formula when Standard deviation is known
UCL =
3D40
A₂ √n
Transcribed Image Text:X bar chart formula when Standard deviation is known Upper control limit (UCL): Lower control limit (LCL): where OF σ = = = σ/√n Standard deviation of distribution of sample means LCL = x+205 ZO = x o = Estimate of the process standard deviation n = Sample size z = Standard normal deviate x = Average of sample means 3D30 42 √n R bar chart formula when Standard deviation is known UCL = 3D40 A₂ √n
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