ME 350: Design for Manufacturability
Turning and Design of Experiments Example
***IMPORTANT: When following this DOE example for your assignment, make sure
that your design matrices are consistent with the ones used for the GCode program.
Design of Experiments Technique
The example problem below is designed to walk you through the DOE analysis.
If you
follow it carefully, the analysis for your lab assignment should be straightforward.
Example Problem
A company which flat rolls steel is having problems with one of its rolling mills.
The
resulting rolled steel has been exhibiting an unacceptably high number of edge cracks.
The variables that affect this process are the draft (the initial thickness minus the final
thickness of the steel), the roll velocity, and the coefficient of friction.
The engineers,
however, do not know how each of these variables affects the number of defects.
In
order to better understand the process the engineers decide to utilize DOE.
For this process, it was decided that a 2
3
factorial design would be performed.
This
means that the three important variables will be examined on two levels each  a low
level (1) and a high level (+1).
The high and low levels should be chosen to create a
range, which encompasses the operating conditions of interest.
Table 3 shows the three
variables and their low and highlevel values.
Variable
Variable Description
Low (1)
High (+1)
x1
Draft (mm)
6
12
x2
Roll velocity (ft/s)
8
12
x3
Coefficient of friction
0.2
0.3
Table 3:
Variable Levels
A complete factorial design contains 2
3
= 8 unique test conditions, so eight experiments
will need to be conducted to collect all of the necessary data.
Table 4 shows the eight
possible test conditions and the resulting number of defects for each condition. If we
were to examine a problem with 4 variables, we would have to set up an experiment with
2
4
= 16 unique test conditions. Remember that we are trying to find the effect of each
term and the effect of the interaction of terms on the end result we are measuring (defects
in this case).
Test
Draft
x1
Roll velocity
x2
Coeff. friction
x3
Defects
d
1
1
1
1
5
2
+1
1
1
18
3
1
+1
1
6
4
+1
+1
1
16
5
1
1
+1
13
6
+1
1
+1
33
7
1
+1
+1
16
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ME 350: Design for Manufacturability
Turning and Design of Experiments Example
8
+1
+1
+1
34
Table 4:
Design Matrix
The information in the design matrix can be represented geometrically as shown in
Figure 1.
Each corner of the cube represents one of the eight test conditions.
The
number of defects, which were observed for each condition, is shown at each corner in
bold.
By using this cube as a tool for examining the data, it can be discovered how each
of the variables affect the number of defects.
For example, by looking at the cube, it can
be seen that there are four opportunities to explore how the number of defects changes
when the coefficient of friction (x3) is changed, and the other variables are held constant.
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 Spring '08
 Staff
 Normal Distribution, Normal probability plot, Experiments Example

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