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

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.

DOE - Terminologies Factors Levels Response

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

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.

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.

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.

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.

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

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)

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%

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

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

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 13.7725 dB (yellow) Average gain for C=1 13.86 dB (blue) Slope= .044

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 14.6625 dB (green) Slope = .85 This tells us that the resistor is a trouble component and causes higher variation in the gain.

Plotting Main Effects of C and R

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

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

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 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

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

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

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