1. DOE – An Effective Tool for Experimental Research
Dr. R. Sudhakaran
Prof & Head
Department of Mechanical Engineering
SNS College of Engineering, Coimbatore

2. Introduction Experiment Design of Experiments
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.

3. DOE - Terminologies
Factors
Levels
Response

4. 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

5. 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.

6. 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.

8. 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.

9. 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.

10. 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

11. 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)

12. 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%

13. Process variables and their levels for Experiments
Parameter
Units
Factor levels -1 +1
Width of the Micro strip μm
9.5 10
10.5
Resistor
Ohms 19 20 21
Capacitor
Milli Farad
500
1000
1500

14. The experiments are conducted eight times to get the gain for all the combination of +1’s and -1’s of the three elements

15. The table below shows that this gain variation (due to C) is .044 dB.
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
dB (yellow)
Average gain for C=1
13.86 dB (blue)
Slope= .044

16. The gain variation due to the Resistor is
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
dB (green)
Slope = .85
This tells us that the resistor is a trouble component and causes higher variation in the gain.

17. Plotting Main Effects of C and R

18. 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
dB (blue)
Average gain for W*R=1
dB (pink)
Slope = .0088

20. Doing the same procedure for all elements and their interactions, we obtain the following results
Obtaining the Rest of the Coefficients

23. 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

24. Limits of Process Variables
Factor
Upper
limit
Lower
Welding
current (I) amps
110 70
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
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

25. Limits of Process Variables
Process parameters
Limits -2 -1 +1 +2
Welding current amps 70 80 90
100
110
Welding Speed mm/min
120
Gas flow rate
Liter/min 5 10 15 20 25
Gun angle Degrees 50 60
Plate Length mm
125
150
175
200

26. 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.

27. 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

28. Quality America – DOE PC –IV software was used to calculate the coefficients.

29. 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

32. Thank You