(DOE) (Analysis of Variance – ANOVA)

61 Pages·2012·1.44 MB·English

3. Design of Experiments (DOE)
(Analysis of Variance – ANOVA)
Hae-Jin Choi
School of Mechanical Engineering,
Chung-Ang University
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What is Design of Experiments (DOE)?
Experiments are used widely in the engineering
n
world
Process characterization & optimization
¨
Evaluation of material properties
¨
Product design & development
¨
Component & system tolerance determination
¨
Design of Experiments (DOE) is;
n
Planning experiments or tests to save resources
¨
(time and money)
Analyzing results of experiments or tests to
¨
characterize your system
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Example: Golfing
How to improve my score in Golfing?
n
Practice!!!
n
Other than that?
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Type of driver used (oversized or regular sized)
¨
Type of ball (2 piece or 3 piece)
¨
Walking or riding cart
¨
Drinking water or beer
¨
Etc…
¨
What combination of the factors is the best for me?
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General model of a process or system
System: function, model, or
n
manufacturing process to
Controllable factors
transform input to output
x1 x2 xp
¨ Golf game
Input: provided materials or
n
energy into the process or system
¨ Physical energy to play golf Response
Response (output): outcome of a Input System (Output)
n
process or performance of a
(Process) y
system
¨ Score
Controllable factors: factors that …..
n
experimenters can control
¨ Driver type, ball type, etc. z1 z2 zq
Uncontrollable factors (noise
n Uncontrollable factors
factors): factors that experiments (Noise factors)
cannot control
¨ Course layout, grass type, weather,
etc.
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What needs to be analyzed?
Determining which variables
n
Controllable factors
are most influential on the
x1 x2 xp
response y
Determining where to set the
n
controllable factors x so that y
Response
Input System (Output)
is almost always near the
(Process) y
desired nominal value
…..
z1 z2 zq
Uncontrollable factors
(Noise factors)
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Experiments with One Factor
Plasma etching process:
n
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Plasma etching process:
An engineer is interested in investigating the relationship
n
between the RF power setting and the etch rate for this tool. The
objective of an experiment like this is to model the relationship
between etch rate and RF power, and to specify the power
setting that will give a desired target etch rate.
The response variable is etch rate.
n
She is interested in a particular gas (C2F6) and gap (0.80 cm),
n
and wants to test four levels of RF power: 160W, 180W, 200W,
and 220W. She decided to test five wafers at each level of RF
power.
The experimenter chooses 4 levels of RF power 160W, 180W,
n
200W, and 220W
The experiment is replicated 5 times – runs made in random
n
order
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Plasma etching process:
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• Does changing the power change the
mean etch rate?
• We would like to have a systematic way
to answer these questions
Analysis of Variance (ANOVA)
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The Analysis of Variance (ANOVA)
In general, there will be a levels of the factor, or a treatments,
n
and n replicates of the experiment, run in random order…a
completely randomized design (CRD)
N = an total runs
n
We consider the fixed effects case…the random effects case
n
will be discussed later
Objective is to test hypotheses about the equality of the a
n
treatment means
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