DOE Steps
Problem statement
Choice of factors, levels, and ranges
Choice of response variable(s)
Choice of experimental design
Performing the experiment
Statistical analysis
Conclusions and recommendations
14

Special Terminology : Design of Experiments
15
Response variable
Measured output value
Factors
Input variables that can be changed
Levels
Specific values of factors (inputs)
Continuous
or discrete
Replication
Completely re-run experiment with same input levels
Used to determine impact of measurement error
Interaction
Effect
of one input factor depends on
level
of another input factor

Major Approaches to DOE
16
Factorial Design
Taguchi Method

17
Factorial Design

Factorial Design : Full factorial design
18A full factorial design of experiments consists of the following:Vary one factor at a timePerform experiments for all levels of all factorsHence perform a large number of experiments that are needed!All interactions are captured.Consider a simple design for the following case:Let the number of factors = kLet the number of levels for the ithfactor = niThe total number of experiments (N) that need to be performed isKiinN1

.

DOE - Factorial Designs - 2
3
20
Trial
A
B
C
1
Lo
Lo
Lo
2
Lo
Lo
Hi
3
Lo
Hi
Lo
4
Lo
Hi
Hi
5
Hi
Lo
Lo
6
Hi
Lo
Hi
7
Hi
Hi
Lo
8
Hi
Hi
Hi

DOE - Factorial Designs - 2
3
21
Trial
A
B
C
1
-1
-1
-1
2
-1
-1
+1
3
-1
+1
-1
4
-1
+1
+1
5
+1
-1
-1
6
+1
-1
+1
7
+1
+1
-1
8
+1
+1
+1

Output Matrix
22
Let us represent the outcome of each experiment to be a quantity
y.
Thus y
1
will represent the outcome of experiment number 1 with
all three
factors having their “LOW
”
values,
y
2
will represent the outcome of the experiment number 2 with
the factors A & B having the
“Low”
values and the factor C
having the
“High”
value and so on.
The outcome of the experiments may be represented as the
following matrix:

Output Matrix
23

24
ANOVA

ANOVA
25

ANOVA
26

ANOVA
27

28
Fractional Factorial Designs

DOE -
Fractional Factorial Designs
29
In a multivariable experiments, with
k
number of variables and
l
number of
levels per variable demands
l
k
number of measurements for complete
understanding of the process or calibration.
In statistics,
fractional factorial designs
are experimental designs consisting of
a carefully chosen subset (fraction) of the experimental runs of a full factorial
design.

#### You've reached the end of your free preview.

Want to read all 46 pages?

- Spring '19
- Magdy Khalaf
- Fractional factorial designs, EFQM Excellence Model