1.
A quality analyst wants to construct a sample mean chart for controlling a packaging
process. He knows from past experience that the process standard deviation is two ounces.
Each day last week, he randomly selected four packages and weighed each. The data from
that activity appears below.
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Package 1
23
23
20
18
18
Weight
Package 2
22
21
19
19
20
Package 3
23
19
20
20
22
Package 4
24
21
21
19
20
(a) Calculate all sample means and the mean of all sample means.
(b) Calculate upper and lower control limits that allow for natural variations.
(c) Is this process in control?
2.
Cartons of Plaster of Paris are supposed to weigh exactly 32 oz. Inspectors want to develop process
control charts. They take ten samples of six boxes each and weigh them. Based on the following
data, compute the lower and upper control limits and determine whether the process is in control.
Sample
Mean
Range
1
2
3
4
5
6
7
8
9
10
33.8
34.6
34.7
34.1
34.2
34.3
33.9
34.1
34.2
34.4
1.1
0.3
0.4
0.7
0.3
0.4
0.5
0.8
0.4
0.3
1
3.
The width of a bronze bar is intended to be one-eighth of an inch (0.125 inches). Inspection
samples contain five bars each. The average range of these samples is 0.01 inches. What are the
upper and lower control limits for the X-bar and R-chart for this process, using 3-sigma limits?
4.
A part that connects two levels should have a distance between the two holes of 4". It has been
determined that X-bar and R-charts should be set up to determine if the process is in statistical
control. The following ten samples of size four were collected. Calculate the control limits, plot
the control charts, and determine if the process is in control.
Sample 1
Sample 2
Sample 3
Sample 4
Sample 5
Sample 6
Sample 7
Sample 8
Sample 9
Sample 10
2
Mean
4.01
3.98
4.00
3.99
4.03
3.97
4.02
3.99
3.98
4.01
Range
0.04
0.06
0.02
0.05
0.06
0.02
0.02
0.04
0.05
0.06