1. Design of Experiment (DOE)
This technique uses experimentation to statistically determine what variables will improve the design or quality of a product. Design of experiments (DOE) is desirable when robust design or quality improvement is required. DOE helps to pin point the sensitive areas in designs that cause problems in production or yield.
2. Example of a DOE Case
DOE was used in the amplifier design process to investigate the sensitivity of this amplifier to process variation. It was necessary to find out the presence of elements in the amplifier design that could potentially affect the output response (http://www.home.agilent.com/upload/cmc_upload/All/DesignOfExperimentsTutorial.pdf?&cc=AE&lc=eng).
3. The Factors, Levels and the Response Variables
In this case, three factors were chosen to investigate their effects on the gain of the amplifier. In this experiment, gain is the outcome that was measured, in other words the response variable. Gain is a measure of the ability of a circuit (the amplifier) to increase the power of a signal from the input to the output, by adding energy to the signal converted from some power supply. The factors chosen for the experiment were: W (the width of the microstrip lines), the resistor (R), and the capacitor (C). Factors are variables under the control of the experimenter that is varied over different experimental units (Schwarz, 279). Factors are assigned levels when designing the experiment. Levels are values of the factor used in the experiment.
4. The experiment
Each factor was assigned a -1 and +1 value. For example the nominal value of the resistor was indicated with a ‘0’. In case of resistor and capacitor a ‘-1’ represents a -5% variation from its nominal value and a ‘+1’ represents a +5% variation from its nominal value. In case of the width of the microstrip lines ‘-1’ corresponds to 9.5 μm, and ‘+1’ corresponds to 10.5 μm, 0 corresponds to nominal value, 10μm. Since three factors and two levels have been chosen, 8 experiments (2^3) were conducted to achieve a full factorial experiment. The factors and the levels used in the experiment are presented in Table 1.
5. Analysis of the Data
The simulation was carried out eight times to get the gain (output measure) for all the combination of ‘+1’s and ‘-1’s of the three factors. The interactions between the factors were also investigated to find out how these interactions affect the variation in the output measure (Gain).
The following linear equation represents the experiment results:
Gain = 13.8 + 0.09W + 0.85R + 0.044C + 0.0088WR + 0.0013 WC + 0.0050RC + 0.0025WRC
It was clear from the above equation that the resistor (R) has the most significant contribution to the gain variability and sensitivity. The impact of other factors such as W, C, WR etc. were insignificant compared to the factor R.
Resistor was found to have the greatest impact on the gain of the amplifier. The other factors and their interactions were found to have insignificant impact compared to the resistor. The designer should stress on his/her efforts in reducing variation due to the resistor. The DOE was a useful tool in pin pointing the factor that had the greatest effect on the output measure or response.
8. Lessons Learned
DOE is a powerful, efficient, scientific approach for optimization of variables at all stages of process development. DOE can help determine how to increase productivity and improve quality. DOE can be used to learn about the process, screen important factors, determine whether factors interact, and optimization the responses (Lye, GC113--3).
9. Follow on experiments
1. Different tolerance of resistor could be used to figure out which tolerance would result in less variation
2. Wider resistor could be used to reduce sensitivity
3. Resistor from different brands could be used to check variability
http://www.home.agilent.com/upload/cmc_upload/All/DesignOfExperimentsTutorial.pdf?&cc=AE&lc=eng. web. 16th April. 2013.
Lye, L. M. “Tools and Toys for Teaching Design of Experiments Methodology”. 33rd Annual General Conference of the Canadian Society for Civil Engineering, 2-4 June 2005: GC113--1-GC113--9. Conference proceedings.
Schwarz, Carl. “Designed Experiments – Terminology and Introduction”. Course Note. Simon Fraser University. December 21, 2012