Baseball circumferences. Baseballs used in the major leagues in the United States must adhere to strict stan- dards. One such standard is that the circumference must be between 9 and 9.25 inches. One could look at this standard as a target circumference of 9.125 inches with a tolerance of +> - 0.125 inches. These data (shown at the bottom of the page) were taken from a random sample of 50 baseballs from a large production batch. The actual circumference and deviation from the target circumference are listed.
Using the specification limits as the control limits,
a) Create a run chart for the baseballs' circumferences.
b) Is the process for making baseballs in terms of their circumference in control?
c) How many baseballs produced were out of spec?
d) When should the quality team have investigated the production process?
|
Sample
|
Circumference
|
Deviation
|
Sample
|
Circumference
|
Deviation
|
|
1
|
8.998
|
- 0.127
|
26
|
9.121
|
- 0.004
|
|
2
|
9.181
|
0.056
|
27
|
9.111
|
- 0.014
|
|
3
|
9.147
|
0.022
|
28
|
9.130
|
0.005
|
|
4
|
9.182
|
0.057
|
29
|
9.116
|
- 0.009
|
|
5
|
9.087
|
- 0.038
|
30
|
9.035
|
- 0.090
|
|
6
|
9.154
|
0.029
|
31
|
9.188
|
0.063
|
|
7
|
9.108
|
- 0.017
|
32
|
9.092
|
- 0.033
|
|
8
|
9.109
|
- 0.016
|
33
|
9.078
|
- 0.047
|
|
9
|
9.141
|
0.016
|
34
|
9.101
|
- 0.024
|
|
10
|
9.093
|
- 0.032
|
35
|
9.113
|
- 0.012
|
|
11
|
9.142
|
0.017
|
36
|
9.087
|
- 0.038
|
|
12
|
9.140
|
0.015
|
37
|
9.054
|
- 0.071
|
|
13
|
9.125
|
0.000
|
38
|
9.177
|
0.052
|
|
14
|
9.175
|
0.050
|
39
|
9.058
|
- 0.067
|
|
15
|
8.985
|
- 0.140
|
40
|
9.179
|
0.054
|
|
16
|
9.119
|
- 0.006
|
41
|
9.147
|
0.022
|
|
17
|
9.140
|
0.015
|
42
|
9.123
|
- 0.002
|
|
18
|
9.109
|
- 0.016
|
43
|
9.097
|
- 0.028
|
|
19
|
9.190
|
0.065
|
44
|
9.108
|
- 0.017
|
|
20
|
9.087
|
- 0.038
|
45
|
9.214
|
0.089
|
|
21
|
9.046
|
- 0.079
|
46
|
9.140
|
0.015
|
|
22
|
9.108
|
- 0.017
|
47
|
9.151
|
0.026
|
|
23
|
9.188
|
0.063
|
48
|
9.041
|
- 0.084
|
|
24
|
9.125
|
0.000
|
49
|
9.061
|
- 0.064
|
|
25
|
9.114
|
- 0.011
|
50
|
9.162
|
0.037
|