Sampling four pieces of precision-cut wire (to be used in computer assembly) eve
ID: 390145 • Letter: S
Question
Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results:
Hour
x
R
Hour
x
R
1
3.25"
0.71"
13
3.11
0.85
2
3.10
1.18
14
2.83
1.31
3
3.22
1.43
15
3.12
1.06
4
3.39
1.26
16
2.84
0.50
5
3.07
1.17
17
2.86
1.43
6
2.86
0.32
18
2.74
1.29
7
3.05
0.53
19
3.41
1.61
8
2.65
1.13
20
2.89
1.09
9
3.02
0.71
21
2.65
1.08
10
2.85
1.33
22
3.28
0.46
11
2.83
1.17
23
2.94
1.58
12
2.97
0.40
24
2.64
0.97
Develop appropriate control limits and determine whether there is any cause for concern in the cutting process.
Hour
x
R
Hour
x
R
1
3.25"
0.71"
13
3.11
0.85
2
3.10
1.18
14
2.83
1.31
3
3.22
1.43
15
3.12
1.06
4
3.39
1.26
16
2.84
0.50
5
3.07
1.17
17
2.86
1.43
6
2.86
0.32
18
2.74
1.29
7
3.05
0.53
19
3.41
1.61
8
2.65
1.13
20
2.89
1.09
9
3.02
0.71
21
2.65
1.08
10
2.85
1.33
22
3.28
0.46
11
2.83
1.17
23
2.94
1.58
12
2.97
0.40
24
2.64
0.97
Explanation / Answer
Solution:
In order to compute the appropriate control limits of the X-bar chart and R chart, the mean X-bar and R-bar needs to be calculated first,
X-bar = Sum of X / Number of observations
X-bar = 71.57 / 24
X-bar = 2.982
R-bar = Sum of R / Number of observations
R-bar = 24.57 / 24
R-bar = 1.024
The Upper Control Limit (UCLx) and Lower Control Limit (LCLx) is calculated as,
UCLx = X-bar + (A2 x R-bar)
LCLx = X-bar - (A2 x R-bar)
The Upper Control Limit (UCLr) and Lower Control Limit (LCLr) is calculated as,
UCLr = D4 x R-bar
LCLr = D3 x R-bar
From the table of factors for computing 3 sigma control chart limits,
For n = 4 (4 pieces of precision cut wire)
A2 = 0.729
D4 = 2.282
D3 = 0
Putting these values in the above formula, we get,
UCLx = 2.982 + (0.729 x 1.024)
UCLx = 3.728
LCLx = 2.982 - (0.729 x 1.024)
LCLx = 2.236
UCLr = 2.282 x 1.024
UCLr = 2.337
LCLr = 0 x 1.024
LCLr = 0
Conclusion: There is no cause for concern in the cutting process. All the 24 observations in the X-bar chart and R-chart lies within the computed values of (UCLx, LCLx) in X-bar chart and within the computed values of (UCLr, LCLr) in R-bar chart.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.