Q6. A quality analyst took the following samples as a pilot study to construct the mean...

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General Management

Q6. A quality analyst took the followingsamples as a pilot study to construct the mean and range charts.The data below shows the weight in ounces. Construct the mean andrange charts showing all control (action) –upper and lower limits,and warning upper and lower limits.
Sample Number
Item1
Item2
Item3
Item4
Sample 1
11.9
12.5
12.4
12.7
Sample 2
12.5
12.5
12.4
12.8
Sample 3
12.2
12.8
12.7
12
Sample 4
12.3
12.4
12.8
12.4
Sample 5
12.1
12.8
12.4
11.9
Sample 6
12.6
12.4
12.1
12.3
The following day, the analyst took another 6 samples to checkif the process under control or not. Theses samples are asfollows:
Sample Number
Item1
Item2
Item3
Item4
Sample 1
11.9
11.5
12.4
12.3
Sample 2
12.5
11.5
13.4
11.8
Sample 3
12.2
11.8
11.7
12
Sample 4
14.3
11.4
11.8
13.4
Sample 5
15.1
11.8
12.4
10.9
Sample 6
11.6
10.4
10.1
15.3
Is the process under control? Why? What actions shouldyou take?
Factors for calculating control limits for control charts
For MEANS
Sample size (n)
Constant (dn)
Factors for warning limits 1.96/dn?n
Factors for action limits 3.09?n
2
1.128
1.23
1.94
3
1.693
0.67
1.05
4
2.059
0.48
0.75
5
2.326
0.38
0.59
6
2.334
0.32
0.50
7
2.704
0.27
0.43
8
2.847
0.24
0.38
9
2.970
0.22
0.35
10
3.078
0.20
0.32
Factors for calculating control limits for control charts
For RANGES
Sample size
Upper warning limit
Lower warning limit
Upper action limit
Lower action limit
2
2.81
0.04
4.12
0.00
3
2.17
0.18
2.98
0.04
4
1.93
0.29
2.57
0.10
5
1.81
0.37
2.34
0.16
6
1.72
0.42
2.21
0.21
7
1.66
0.46
2.11
0.26
8
1.62
0.50
2.04
0.29
9
1.58
0.52
1.99
0.32
10
1.56
0.54
1.94
0.35

Answer & Explanation Solved by verified expert

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Sample NoItem1Item2Item3Item4Sample MeanSample RangeSample 111901250124012701238080Sample 212501250124012801255040Sample 312201280127012001243080Sample See Answer

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Sample Number	Item1	Item2	Item3	Item4
Sample 1	11.9	12.5	12.4	12.7
Sample 2	12.5	12.5	12.4	12.8
Sample 3	12.2	12.8	12.7	12
Sample 4	12.3	12.4	12.8	12.4
Sample 5	12.1	12.8	12.4	11.9
Sample 6	12.6	12.4	12.1	12.3

Sample size (n)	Constant (dn)	Factors for warning limits 1.96/dn?n	Factors for action limits 3.09?n
2	1.128	1.23	1.94
3	1.693	0.67	1.05
4	2.059	0.48	0.75
5	2.326	0.38	0.59
6	2.334	0.32	0.50
7	2.704	0.27	0.43
8	2.847	0.24	0.38
9	2.970	0.22	0.35
10	3.078	0.20	0.32

Sample size	Upper warning limit	Lower warning limit	Upper action limit	Lower action limit
2	2.81	0.04	4.12	0.00
3	2.17	0.18	2.98	0.04
4	1.93	0.29	2.57	0.10
5	1.81	0.37	2.34	0.16
6	1.72	0.42	2.21	0.21
7	1.66	0.46	2.11	0.26
8	1.62	0.50	2.04	0.29
9	1.58	0.52	1.99	0.32
10	1.56	0.54	1.94	0.35