The data in Table 3 are the tensile strengths of bolts of cloth. The data were c
ID: 454232 • Letter: T
Question
The data in Table 3 are the tensile strengths of bolts of cloth. The data were collected in subgroups of 4 bolts of cloth over a 30 hour period.
Table 3
Sample
Strength
Sample
Strength
Sample
Strength
1
21.91
11
21.63
21
22.33
1
21.59
11
23.36
21
22.10
1
21.07
11
22.38
21
22.03
1
21.83
11
22.37
21
22.15
2
22.51
12
22.33
22
22.52
2
22.49
12
22.12
22
23.17
2
22.38
12
21.60
22
22.14
2
21.57
12
22.32
22
22.47
3
22.28
13
21.81
23
22.66
3
21.70
13
21.72
23
21.71
3
21.98
13
22.68
23
22.57
3
22.35
13
22.66
23
21.36
4
22.43
14
22.30
24
22.22
4
21.37
14
22.97
24
22.09
4
22.39
14
22.68
24
22.36
4
21.84
14
22.44
24
21.46
5
22.02
15
21.97
25
21.63
5
22.02
15
20.92
25
21.64
5
22.14
15
22.38
25
22.28
5
22.37
15
22.37
25
22.45
6
21.88
16
22.50
26
22.79
6
21.74
16
21.97
26
22.64
6
23.01
16
22.36
26
22.78
6
22.10
16
22.91
26
21.99
7
21.87
17
21.71
27
21.75
7
22.49
17
23.12
27
21.34
7
21.39
17
21.58
27
22.54
7
21.95
17
21.89
27
21.81
8
22.09
18
21.83
28
21.99
8
22.14
18
21.19
28
21.62
8
22.12
18
21.87
28
21.35
8
21.25
18
22.22
28
21.54
9
22.33
19
22.85
29
21.38
9
22.46
19
22.64
29
22.16
9
22.74
19
21.70
29
22.16
9
21.56
19
21.43
29
22.84
10
22.21
20
22.23
30
22.04
10
22.00
20
22.90
30
21.95
10
22.25
20
22.01
30
21.84
10
22.65
20
21.92
30
21.90
(a) Suppose the LSL and the USL for tensile strength are 19.8 and 24.2. (i) Is the process able to meet specification limits at the four-sigma standard?(ii) Is the process capable in terms of actual process performance at the four-sigma standard?
(b) Do you have any concerns about the conclusions made in part (b)?
Sample
Strength
Sample
Strength
Sample
Strength
1
21.91
11
21.63
21
22.33
1
21.59
11
23.36
21
22.10
1
21.07
11
22.38
21
22.03
1
21.83
11
22.37
21
22.15
2
22.51
12
22.33
22
22.52
2
22.49
12
22.12
22
23.17
2
22.38
12
21.60
22
22.14
2
21.57
12
22.32
22
22.47
3
22.28
13
21.81
23
22.66
3
21.70
13
21.72
23
21.71
3
21.98
13
22.68
23
22.57
3
22.35
13
22.66
23
21.36
4
22.43
14
22.30
24
22.22
4
21.37
14
22.97
24
22.09
4
22.39
14
22.68
24
22.36
4
21.84
14
22.44
24
21.46
5
22.02
15
21.97
25
21.63
5
22.02
15
20.92
25
21.64
5
22.14
15
22.38
25
22.28
5
22.37
15
22.37
25
22.45
6
21.88
16
22.50
26
22.79
6
21.74
16
21.97
26
22.64
6
23.01
16
22.36
26
22.78
6
22.10
16
22.91
26
21.99
7
21.87
17
21.71
27
21.75
7
22.49
17
23.12
27
21.34
7
21.39
17
21.58
27
22.54
7
21.95
17
21.89
27
21.81
8
22.09
18
21.83
28
21.99
8
22.14
18
21.19
28
21.62
8
22.12
18
21.87
28
21.35
8
21.25
18
22.22
28
21.54
9
22.33
19
22.85
29
21.38
9
22.46
19
22.64
29
22.16
9
22.74
19
21.70
29
22.16
9
21.56
19
21.43
29
22.84
10
22.21
20
22.23
30
22.04
10
22.00
20
22.90
30
21.95
10
22.25
20
22.01
30
21.84
10
22.65
20
21.92
30
21.90
Explanation / Answer
Given that LSL = 19.8 and USL = 24.2
Grand mean of the samples is 22.11717 and the standard deviation of sample observations is .474847.
Four sigma specification is having probability of 99.994% or .99994 or 60 (approx.) DPMO (defects per million opportunities.
Therefore mean tensile strength is to be in the range 22.11717 - 4*.474847 and 22.11717 + 4*.474847
Which is 20.21778 to 24.01655 whereas the given LSL is lower than the calculated limit , similarly the calculated upper limit is less than the USL, therefore the process is capable of meeting the specification limits at the four sigma.
(ii) The process is capable in terms of actual process performance at the four-sigma standard as shown below:
Question itself is marked as (b) and concerns about conclusions made in part (b) No concerns, may be more values above central line and towards USL as compared to LSL.
Sample Strength Actual-LSL USL- Actual 1 21.91 1.69222 2.10655 1 21.59 1.37222 2.42655 1 21.07 0.85222 2.94655 1 21.83 1.61222 2.18655 2 22.51 2.29222 1.50655 2 22.49 2.27222 1.52655 2 22.38 2.16222 1.63655 2 21.57 1.35222 2.44655 3 22.28 2.06222 1.73655 3 21.7 1.48222 2.31655 3 21.98 1.76222 2.03655 3 22.35 2.13222 1.66655 4 22.43 2.21222 1.58655 4 21.37 1.15222 2.64655 4 22.39 2.17222 1.62655 4 21.84 1.62222 2.17655 5 22.02 1.80222 1.99655 5 22.02 1.80222 1.99655 5 22.14 1.92222 1.87655 5 22.37 2.15222 1.64655 6 21.88 1.66222 2.13655 6 21.74 1.52222 2.27655 6 23.01 2.79222 1.00655 6 22.1 1.88222 1.91655 7 21.87 1.65222 2.14655 7 22.49 2.27222 1.52655 7 21.39 1.17222 2.62655 7 21.95 1.73222 2.06655 8 22.09 1.87222 1.92655 8 22.14 1.92222 1.87655 8 22.12 1.90222 1.89655 8 21.25 1.03222 2.76655 9 22.33 2.11222 1.68655 9 22.46 2.24222 1.55655 9 22.74 2.52222 1.27655 9 21.56 1.34222 2.45655 10 22.21 1.99222 1.80655 10 22 1.78222 2.01655 10 22.25 2.03222 1.76655 10 22.65 2.43222 1.36655 11 21.63 1.41222 2.38655 11 23.36 3.14222 0.65655 11 22.38 2.16222 1.63655 11 22.37 2.15222 1.64655 12 22.33 2.11222 1.68655 12 22.12 1.90222 1.89655 12 21.6 1.38222 2.41655 12 22.32 2.10222 1.69655 13 21.81 1.59222 2.20655 13 21.72 1.50222 2.29655 13 22.68 2.46222 1.33655 13 22.66 2.44222 1.35655 14 22.3 2.08222 1.71655 14 22.97 2.75222 1.04655 14 22.68 2.46222 1.33655 14 22.44 2.22222 1.57655 15 21.97 1.75222 2.04655 15 20.92 0.70222 3.09655 15 22.38 2.16222 1.63655 15 22.37 2.15222 1.64655 16 22.5 2.28222 1.51655 16 21.97 1.75222 2.04655 16 22.36 2.14222 1.65655 16 22.91 2.69222 1.10655 17 21.71 1.49222 2.30655 17 23.12 2.90222 0.89655 17 21.58 1.36222 2.43655 17 21.89 1.67222 2.12655 18 21.83 1.61222 2.18655 18 21.19 0.97222 2.82655 18 21.87 1.65222 2.14655 18 22.22 2.00222 1.79655 19 22.85 2.63222 1.16655 19 22.64 2.42222 1.37655 19 21.7 1.48222 2.31655 19 21.43 1.21222 2.58655 20 22.23 2.01222 1.78655 20 22.9 2.68222 1.11655 20 22.01 1.79222 2.00655 20 21.92 1.70222 2.09655 21 22.33 2.11222 1.68655 21 22.1 1.88222 1.91655 21 22.03 1.81222 1.98655 21 22.15 1.93222 1.86655 22 22.52 2.30222 1.49655 22 23.17 2.95222 0.84655 22 22.14 1.92222 1.87655 22 22.47 2.25222 1.54655 23 22.66 2.44222 1.35655 23 21.71 1.49222 2.30655 23 22.57 2.35222 1.44655 23 21.36 1.14222 2.65655 24 22.22 2.00222 1.79655 24 22.09 1.87222 1.92655 24 22.36 2.14222 1.65655 24 21.46 1.24222 2.55655 25 21.63 1.41222 2.38655 25 21.64 1.42222 2.37655 25 22.28 2.06222 1.73655 25 22.45 2.23222 1.56655 26 22.79 2.57222 1.22655 26 22.64 2.42222 1.37655 26 22.78 2.56222 1.23655 26 21.99 1.77222 2.02655 27 21.75 1.53222 2.26655 27 21.34 1.12222 2.67655 27 22.54 2.32222 1.47655 27 21.81 1.59222 2.20655 28 21.99 1.77222 2.02655 28 21.62 1.40222 2.39655 28 21.35 1.13222 2.66655 28 21.54 1.32222 2.47655 29 21.38 1.16222 2.63655 29 22.16 1.94222 1.85655 29 22.16 1.94222 1.85655 29 22.84 2.62222 1.17655 30 22.04 1.82222 1.97655 30 21.95 1.73222 2.06655 30 21.84 1.62222 2.17655 30 21.9 1.68222 2.11655Related Questions
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