Task:
A company has recently invested in a new machine and wants to compare its performance to an
old machine of the same type that they have had for a long time. During an afternoon they
observe 20 units of the same product produced in the two machines and record the measure Yi
(i = 1, 2). They also observe the corresponding value of a control parameter Xi , which according to
the manufacturer of the machines, is suitable for controlling the outcome of the studied measure Yi .
The table below shows the results for the two machines. Are there any differences in performance
between the two machines? Is Xi a suitable control parameter for Yi ?
New machine
X1
Y1
19.6
47.9
20.2
51.3
20.6
53.0
20.3
50.0
20.4
53.1
21.8
49.8
19.9
47.4
19.3
47.2
26.5
56.8
25.1
58.1
22.1
51.3
23.2
55.1
21.7
48.3
22.4
45.6
21.6
48.8
23.9
50.9
21.9
55.4
22.9
51.8
21.9
49.4
21.8
52.6
Old machine
X2
Y2
21.1
52.1
22.5
54.7
21.6
52.9
23.5
55.9
21.5
52.9
23.2
56.5
22.5
54.7
23.6
56.7
22.8
55.7
21.3
52.4
22.2
53.1
22.6
54.9
22.1
54.8
20.9
52.6
22.1
53.7
22.8
55.1
22.5
55.9
21.6
53.9
23.5
56.8
23.0
55.2
1
Solution:
The histograms indicate that the variability is much larger for the old machine (i = 1). Moreover,
the mean value of Y also seem to differ, with E[Y2 ] > E[Y1 ].
Histogram old machine
Histogram new machine
0.3
0.3
0.2
0.2
0.1
0.1
0
44
48
52
56
0
44
60
48
52
56
60
To investigate if X is a good control parameter for Y scatter plots may be used, where Y is plotted
against X. If Y depends on X there should be a non-random pattern. The plots indicate that X
is a better control parameter for Y on the new machine!
60
57
58
56
56
55
Y2
Y1
54
52
54
50
48
53
46
18
20
22
24
26
52
20
28
X1
2
20.5
21
21.5
22
X2
22.5
23
23.5
24