Transcript An Effective Tool for Experimental Research

DOE – An Effective Tool for Experimental
Research
Dr. R. Sudhakaran
Prof & Head
Department of Mechanical Engineering
SNS College of Engineering, Coimbatore
1
Introduction
• Experiment
– Systematic procedure carried out under controlled
conditions to determine an known/unknown effect, to
test or establish a hypothesis
– Used to evaluate the impact of process inputs on the
process outputs
– Determine the target level of inputs to achieve a
desired result
• Design of Experiments
– DOE is a formal mathematical method for
systematically planning and conducting scientific
studies that change experimental variables together
in order to determine their effect of a given response.
2
DOE - Terminologies
• Factors
• Levels
• Response
3
Designed experiments - Uses
– Comparing Alternatives – In cake baking, comparing
results from two different types of flour
– Identifying the significant inputs affecting an output
– Achieving an optimal process output – How to get
exact taste and consistency in Chocolate cake
– Targeting an output – How to make a cake as moist
as possible without disintegrating
– Improving process or product robustness – Can the
factors and levels be modified – Cake will come out
neatly the same
– Balancing tradeoffs – Multiple critical quality
characteristics that require optimization – “ How to
produce best quality cake with simplest recipe and
short baking time
4
• The Design of an experiment addresses the
questions outlined by stipulating the
following:
• The factors to be tested.
• The levels of those factors.
• The structure and layout of experimental
runs, or conditions.
• A well-designed experiment is as simple as
possible - obtaining the required information
in a cost effective and reproducible manner.
5
BASIC STEPS IN DOE
• Four elements associated with DOE:
– The design of the experiment,
– The collection of the data,
– The statistical analysis of the data, and
– The conclusions reached and
recommendations made as a result of the
experiment.
6
7
PLANNING A DOE
• Everyone involved in the experiment should have a clear
idea in advance of exactly
– What is to be studied?
– The objectives of the experiment
– The questions one hopes to answer and
– The results anticipated
• Select a response/dependent variable (variables) that
will provide information about the problem under study.
• Select a proposed measurement method for this
response variable, including an understanding of the
measurement system variability.
8
PLANNING A DOE
• Select the independent variables (factors), the number of
levels for each factor and the levels of each factor.
• Choose an appropriate experimental design that will
allow your experimental questions to be answered once
the data is collected and analyzed.
• Perform the experiment (collect data) paying particular
attention to measurement system accuracy, while
maintaining as uniform an experimental environment as
possible.
9
PLANNING A DOE
• Analyze the data using the appropriate
regression model insuring that attention is paid
to checking the model accuracy.
• Based on the results of the analysis,
– draw conclusions/inferences about the results,
– interpret the physical meaning of these results,
– determine the practical significance of the findings,
and make recommendations for a course of action
10
Case Study - Amplifier
• Objective- To investigate sensitivity of the
amplifier due to process variation
• Factors
– Width of the micro strip lines (W)
– Resistor (R)
– Capacitor (c)
• Response
– Gain of the amplifier (G)
11
Choose three variables with their +1 and -1 :
Width of lines (W) W=W_nominal ± .5 um
Resistors (R) R = R_nominal ± 5%
Capacitors (C) C = C_nominal ± 5%
12
Process variables and their
levels for Experiments
Parameter
Units
Width of the
μm
Micro strip
Resistor
Capacitor
Ohms
Milli
Farad
Factor levels
-1
9.5
0
10
+1
10.5
19
500
20
1000
21
1500
13
• The experiments are conducted eight
times to get the gain for all the
combination of +1’s and -1’s of the three
elements
14
• Main effects of Capacitor, C on the Gain. We calculate
the average Gain when C is “-1” and when C is “+1” and
determine the total gain variation due to the Capacitor.
• The table below shows that this gain variation (due to C)
is .044 dB.
Average gain for C=-1
13.7725 dB (yellow)
Average gain for C=1
13.86 dB (blue)
Slope= .044
15
• The gain variation due to the Resistor is
.85 dB, which is much higher than that of
the Capacitor.
Average gain for R=-1
12.97 dB (blue)
Average gain for R=1
14.6625 dB (green)
Slope = .85
• This tells us that the resistor is a trouble
component and causes higher variation in
the gain.
16
Plotting Main Effects of C and R
17
• DOE is also very useful in getting information on the
interactions between the elements in a design and how
these interactions affect the variation in the output
Average gain for W*R=-1
13.8075 dB (blue)
Average gain for W*R=1
13.825 dB (pink)
Slope = .0088
18
19
• Doing the same procedure for all elements and their
interactions, we obtain the following results
• Obtaining the Rest of the Coefficients
20
21
22
Plan of Work
Identifying the process variables
Developing the design matrix
Conducting the experiments as per the design matrix
Development of mathematical models
Evaluation of coefficients of the models
Checking adequacy of the models
Testing the regression coefficients of the models
Validation of the mathematical models
Analyzing the results
Limits of Process Variables
• The angular distortion is
a function of many
independently
controllable process
parameters such as
welding current (I),
welding speed (V), gas
flow rate (Q), gun angle
(θ), plate length (L)
• The design plan was
decided based on the
practical considerations
for the system
Factor
Upper
limit
Lower
limit
Welding
current (I) amps
110
70
Welding
speed (V)
mm/min
120
80
Gas flow rate (Q)
liter/min
25
5
Gun
Angle (θ)
Degrees
90
50
Plate Length (L)
mm
200
100
Limits of Process Variables
Process
parameters
Limits
-2
-1
0
+1
+2
Welding
current amps
70
80
90
100
110
Welding Speed
mm/min
80
90
100
110
120
Gas flow rate
Liter/min
5
10
15
20
25
Gun angle
Degrees
50
60
70
80
90
Plate Length
mm
100
125
150
175
200
Design Matrix
The design matrix chosen to
conduct the experiments was
five factor, five levels central
composite rotatable designs
consisting of 32 sets of coded
conditions .
This design matrix comprises
a full replication factorial
design i.e. 24 = 16 factorial
design plus 7 center points
and 8 star points.
Evaluation of Regression
Coefficients
The response
function can be
expressed as α =f (θ,
V, L, I, Q) and the
relationship selected
is a second order
response surface.
The function is as
follows
• Quality America – DOE PC –IV software was used
to calculate the coefficients.
Development of Mathematical
Model
• Insignificant
coefficients were
dropped along with the
parameters with which
they are associated.
• This was carried out by
conducting backward
elimination analysis
with t- probability
criterion kept at 0.75
• The final mathematical
model is as follows
30
31
Thank You
32