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# Basics Of Robust Design For DFSS

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Most of us are wrongly taught that robust design (of DFSS) can only be achieved through experimental methods like DOE and Taguchi. It's a time consuming approach and it's been known for a while that it's very limited.

What's more, robust design is significantly easier to understand visually and can also be done easily and quickly mathematically by simply looking at an equation. Let's see how.

Consider the formula below. It is for the stiffness of a simple helical spring.
We want a certain spring rate k.

The question we are now faced with is: what values should we select for each of the input variables to minimise the effects of randomness (or have a robust design)?

Consider the graph below.

Note how when we have a smaller gradient (blue) the variability is compressed, but with a larger gradient (red) it is expanded? Well that's basically robustification: finding the smaller gradient.

So now back to the spring. Let's consider each variable and it's gradient:

• The spring diameter D Increasing the value will quickly reduce the gradient; it is inverse and cubed
• The wire diameter d Decreasing it will reduce the gradient very quickly because it is quatic
• The modulus of rigidity G The gradient doesn't change because it is linear
• The number of coils n Increasing the value decreases the gradient fairly quickly; it is reciprocated

Therefore, the easiest way to robustify this design is to: minimise d, maximise D, maximise n and then adjust G to provide the desired k value.

Now obviously this is a simple example, and you will probably have something more sophisticated. Nevertheless, what I have explained to you here is enough so that you can now understand the mathematics of how a system is easily robustified. Without costly experiments. Remember, it is all about the gradient.

So why don't we know more about these simple and easy probabilistic methods? probably because the quality industry is still dominated by by statistitians who are basically experimentalists.

They key is to become familiar with principles of probabilistic design methods and robustification. Once you have, you can intuitively apply these principles. And produce quality designs with ease. If you want to improve your understanding of how probability and mathematics can help you easily improve quality and achieve six sigma, then you can learn more here. You can sign up to a free theory update about probabilistic design, download some free software and get a free sample of of an e-book on probabilistic design.

Please let me know if you have any questions about this. I think a lot of people are let down by not being taught this stuff, and I really want to rectify this situation.

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Thanks for this post Clint. I agree with you - many people are not exposed to tolerance generation through basics of robust design.

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