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November 22, 2010 - 8:45am
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Using Design of Experiments for integration of Subs into Main speaker systems (For JA in particular)
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Design of Experiments (DOE) Tutorial from the American Society of Quality
Description
Design of experiments (DOE) is a powerful tool that can be used in a variety of experimental situations. DOE allows for multiple input factors to be manipulated determining their effect on a desired output (response). By manipulating multiple inputs at the same time, DOE can identify important interactions that may be missed when experimenting with one factor at a time. All possible combinations can be investigated (full factorial) or only a portion of the possible combinations (fractional factorial). Fractional factorials will not be discussed here.
When to Use DOE
Use DOE when more than one input factor is suspected of influencing an output. For example, it may be desirable to understand the effect of temperature and pressure on the strength of a glue bond.
DOE can also be used to confirm suspected input/output relationships and to develop a predictive equation suitable for performing what-if analysis.
DOE Procedure
Acquire a full understanding of the inputs and outputs being investigated. A process flow diagram or process map can be helpful. Utilize subject matter experts as necessary.
Determine the appropriate measure for the output. A variable measure is preferable. Attribute measures (pass/fail) should be avoided. Ensure the measurement system is stable and repeatable.
Create a design matrix for the factors being investigated. The design matrix will show all possible combinations of high and low levels for each input factor. These high and low levels can be generically coded as +1 and -1. For example, a 2 factor experiment will require 4 experimental runs
..........................Input A Level.......Input B Level
Experiment #1.........-1......................-1
Experiment #2........-1......................+1
Experiment #3.......+1.......................-1
Experiment #4 ......+1......................+1
Note: The required number of experimental runs can be calculated using the formula 2n where n is the number of factors.
For each input, determine the extreme but realistic high and low levels you wish to investigate. In some cases the extreme levels may be beyond what is currently in use. The extreme levels selected should be realistic, not absurd. For example:
Enter the factors and levels for the experiment into the design matrix. Perform each experiment and record the results. For example:
Factors................Input -1 Level.......Input +1 Level
Temperature........100 degrees.........200 degrees
Pressure..............50 psi.................100 psi
Calculate the effect of a factor by averaging the data collected at the low level and subtracting it from the average of the data collected at the high level. For example:
Effect of Temperature on strength:
(51 + 57)/2 - (21 + 42)/2 = 22.5 lbs
Effect of Pressure on strength:
(42 + 57)/2 - (21 + 51)/2 = 13.5 lbs
The interaction between two factors can be calculated in the same fashion. First, the design matrix must be amended to show the high and low levels of the interaction. The levels are calculated by multiplying the coded levels for the input factors acting in the interaction. For example:
..........................Input A Level............Input B Level....Interaction
Experiment #1.....-1.............................-1.................+1
Experiment #2.....-1............................+1.................-1
Experiment #3.....+1............................-1................. -1
Experiment #4.....+1...........................+1.................+1
Calculate the effect of the interaction as before.
Effect of the interaction on strength:
(21 + 57)/2 - (42 + 51)/2 = -7.5 lbs
The experimental data can be plotted in a 3D Bar Chart.
http://photos.imageevent.com/puma_cat/fujif31andf20photos/doe-tutorial1.gif
The effect of each factor can be plotted in a Pareto Chart.
http://photos.imageevent.com/puma_cat/fujif31andf20photos/doe-tutorial2.gif
The negative effect of the interaction is most easily seen when the pressure is set to 50 psi and Temperature is set to 100 degrees. Keeping the temperature at 200 degrees will avoid the negative effect of the interaction and help ensure a strong glue bond.
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This simple-minded example above shows that there is an interaction between temperature and pressure in the strength of the glue bond. This is one feature of DOEs that is particularly useful when looking at the effect of a number of factors and their effect on the critical functional response.
Now that that is out of the way as intro, let's look at the specific experiment I had in mind in the next post.
I look forward to the full story!
Of great interest will be what your ears tell you and comparing that to what your calculations predict.
Buddha,
I've been meaning to do that, but I haven't figured out how to embed graphics into forum posts yet....and my Design of Experiments results, which are written up, are graphics-rich.
Perhaps Stephen Mejias can provide some tips...
[image]http://ecx.images-amazon.com/images/I/41H%2BlokzOIL._AA300_.jpg[/image]
The classic DOE uses various combinations of factors and test the extremes so that the landscape of responses is mapped from which you get the optimal result. The example shown with two levels used four experiments. With many levels (or factors) the experiments increase very quickly. A seven factor test will require 128 experiments for a full DOE.
I have used the above methods for few factors. For seven factors, I have used the Taguchi Method where only eight experiments would be needed. What is sacrificed is some of the interactions, and other things I have not taken the time to fully understand. But it works! You may not get the best "optimum", but can get pretty close to it with a lot less work. Then a confirmation test is done to show that it works. It also shows which factors are most influential. Then you can run a smaller full DOE on those to get to the best solution.
One can measure the result and correlate it with listening evaluations. Looking forward to the results and your impressions.
This approach assumes several things about the system under test, assumptions that may not be realistic:
If only life were so simple. Voicing the hifi setup takes great patience, and one cannot hope to find the ultimate optimum setup in any given room. DOE may be of limited help and should be exercised over quite small variations. And then still, how to evaluate and quantify the result of each experiment?
Just keep listening, use knowledge of acoustics as best as we can understand, and enjoy the process. It may go on for quite awhile.