A process that is considered to be in control measures an ingredient in ounces.
ID: 2417015 • Letter: A
Question
A process that is considered to be in control measures an ingredient in ounces. Below are the last 10 samples (each of size n=5) taken.
The population process standard deviation, is 1.36.
Samples
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2
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10
10
13
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8
12
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If z = 3, what are the control limits for the mean chart?
What are the control limits for the range chart?
Is the process in control?
Please show all work. Thanks
Samples
1
2
3
4
5
6
7
8
9
10
10
9
13
10
12
10
10
13
8
10
9
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10
11
10
8
12
10
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10
11
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8
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8
12
9
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8
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8
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12
Explanation / Answer
Processes Samples Mean Range 1 10 9 10 9 12 10 3 2 9 9 11 11 10 10 3 3 13 9 10 10 9 10.2 4 4 10 10 11 10 10 10.2 1 5 12 10 9 11 10 10.4 3 6 10 10 8 12 9 9.8 4 7 10 11 10 8 9 9.6 3 8 13 10 8 10 8 9.8 5 9 8 8 12 12 9 9.8 4 10 10 12 9 8 12 10.2 4 Average 10 3.4 Control Limits of Mean Chart if z=3 Upper Control Limit(UCL)= Mean + z*S.D = 10+3*1.36 14.08 Lower Control Limit(LCL)= Mean - z*S.D = 10-(3*1.36) Three-sigma Factor Table 5.92 sample size A-factor B-factor(D3) C-factor(D4) 2 1.88 0 3.268 Control Limits for Range Chart: 3 1.023 0 2.574 4 0.729 0 2.282 Upper Control Limit(UCL)=D4*R 5 0.577 0 2.114 = 2.114*3.4 6 0.483 0 2.004 7.1876 7 0.419 0.076 1.924 8 0.373 0.136 1.864 Lower Control Limit(UCL)=D3*R 9 0.337 0.184 1.816 = 0*3.4 10 0.308 0.233 1.777 0 Since the values are between the control limits this process is controllable Note: Mean is equal to average of the all samples Range means difference between the Highest and lowest sample of the process
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