A production manager at Ultra Clean Dishwashing Company is monitoring the quality of the company's production process.
There has been concern relative to the quality of the operation to accurately fill the 16 ounces of dishwashing liquid.
A common requirement in this industry shows that the tolerance should be 10% of the expected volume (±10%). The study of the production process returns the process mean (15.8) and standard deviation (0.6).
What is the probability of generating a defect?
Is the process capable?
Table: Factors for three-sigma control limits of Sand R-charts
|
Factor for -Chart
|
Factors for R-Chart
|
|
Sample Size n
|
A2
|
D3
|
D4
|
|
2
|
1.88
|
0
|
3.27
|
|
3
|
1.02
|
0
|
2.57
|
|
4
|
0.73
|
0
|
2.28
|
|
5
|
0.58
|
0
|
2.11
|
|
6
|
0.48
|
0
|
2.00
|
|
7
|
0.42
|
0.08
|
1.92
|
|
8
|
0.37
|
0.14
|
1.86
|
|
9
|
0.34
|
0.18
|
1.82
|
|
10
|
0.31
|
0.22
|
1.78
|
|
11
|
0.29
|
0.26
|
1.74
|
|
12
|
0.27
|
0.28
|
1.72
|
|
13
|
0.25
|
0.31
|
1.69
|
|
14
|
0.24
|
0.33
|
1.67
|
|
15
|
0.22
|
0.35
|
1.65
|
|
16
|
0.21
|
0.36
|
1.64
|
|
17
|
0.20
|
0.38
|
1.62
|
|
18
|
0.19
|
0.39
|
1.61
|
|
19
|
0.19
|
0.40
|
1.60
|
|
20
|
0.18
|
0.41
|
1.59
|
|
21
|
0.17
|
0.43
|
1.58
|
|
22
|
0.17
|
0.43
|
1.57
|
|
23
|
0.16
|
0.44
|
1.56
|
|
24
|
0.16
|
0.45
|
1.55
|
|
25
|
0.15
|
0.46
|
1.54
|
Source: Factors adapted from the ASTM Manual on Quality Control of Materials.