DoE 03

How you should apply virtual DoE in the design process

You are reading the third part of an article trilogy about Design of Experiments (DoE). The trilogy covers the why, when and how to perform virtual DoE in the design process. By following these guidelines, you will experience a faster, smarter and cheaper way to get results that are vastly more reliable and ultimately a greater chance of succeeding with your product.

In the following, we will focus on how to apply virtual DoE to your design process, by starting early, work systematically and evaluate which tests to perform on your product.


Virtual DoEs can be applied early in the development process, and can be leveraged for a fraction of the cost of physical DoEs. Verification of the numbers, resulting from your virtual tests is essential though, for you might have missed something crucial.


Let us dive into a specific example: for simplicity, consider a simple snap hook connection. We decide on three variables, which we think could have an influence on the disengagement force.

Snap hook 1

If we were to conduct actual, physical experiments, one would typically vary each factor in two or three levels, sometimes more. For each variant, a new injection molding tool would need to be manufactured (or at least modifying an existing prototype mold several times), each sample would undergo verification to ensure that the selected are factors are as specified in the test plan, and of course, all measurement equipment must be calibrated and validated.

If you have run a screening experiment, meaning you only varied each factor in two levels, only the relative importances of the factors can be detected. If we have three levels, we begin to see some curvature (if there is any), and then there is random error, which must be taken into account by replicating the experiments several times.


The difference lies in the test schemes
See the difference between the two test designs below?

DoE graph 1

The left one is a commonly used design for physical experiments (a so-called central composite design is shown in this case. Many other designs are available) and the right one is a test design more suited for computer experiments. In the former case, two factors, X1 and X2, are varied, where the design points lie on a circle. The resulting metamodel would in this case be a simple second-order model, which detects monotonic curvature (i.e. the analysis program performs quadratic regression, which requires at least three data points for each factors). The computer-optimized models, on the other hand, allow us to detect more complex behaviors, owing to their higher resolution.

Instead of having two or three levels per factor, each factor is varied in as many levels as there are experimental runs. Therefore, if we decide to run 20 experiments, we would also have 20 different variants of each factor tested. This provides a vastly more detailed insight into the underlying the phenomena, governing the product performance. This is illustrated below. Note how the closely spaced design points provide a much better basis for interpolation and allows for fitting higher order nonlinear models rather than just second-order polynomial models.

DoE graph 2

The snap mechanism outlined before had three factors. We know from basic mechanics that the deflection distance of a cantilever snap has a linear relationship to the disassembly force, while the angle and length of snap arm has a trigonometrical and third-order relationship, respectively. These behaviors can be captured using computer experiments, providing a high resolution and thus more insight into the ‘temperament’, or volatility, of the different factors.


Virtual testing can never replace real-life tests fully – but we can still gain insight for qualification of concepts
Again, using caution and engineering judgment is crucial, even in this simple cantilever snap example. For instance, we did not consider the thickness of the snap arm, nor did we take material properties into account. Polymers are seldom linear in behavior, and factors such as strain rate, temperature and time may have significant impact.

Secondly, George Box’ quote, “essentially, all models are wrong, but some are useful” could very well be applied to CAD models as well. After all, these are just representations of what the real product should look like, though the reality might be very different, as seen on the comparison between a CAD model of a snap detail and its real-life molded counterpart.

Snap hook 2

Parting lines in the mold, its general layout, and process settings all have an influence on how the virtual CAD model translates into your real-life product. See the flash on the bottom of the snap head slope? This defect could potentially add length to the deflection distance – one of the three factors, we tested for. Performing real-life tests is therefore indispensable and virtual testing must not act as replacement hereof, at least not completely.

To sum up, there is a plethora of virtual DoE designs that can be applied to gain early insight, and at a lower cost, but applying engineering experience and judgment is essential to ensure useful and reliable results.

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