What is Robust Design?

Robust Design is a technique by which you can optimize a product so that its behavior is not only improved, but more predictable. In DesignXplorer, the product behavior is expressed using the response parameters you choose. For example, in a finite model, you might use the maximum stress or maximum deflection to decide whether the product behavior is acceptable.

Robust Design is based on assumptions regarding scatter, or uncontrollable uncertainties. Scatter in the input parameters that affect the response parameters will cause the response parameters to also be uncertain and therefore less predictable. Robust Design is based on the result parameters of a Six Sigma Analysis. Therefore, before you run a Robust Design analysis, you must first parameterize the results of a Six Sigma Analysis. To understand which Six Sigma Analysis parameters should be parameterized, look at how robustness can be defined and measured.

• Reduction of Variability: If the input parameters that affect response parameters are subjected to uncertainty and scatter, the response parameters are also uncertain; i.e., they will show variability to some degree. Used to reduce the variability of product behavior, you can use the following Six Sigma Analysis result parameters:

• Standard Deviation: The standard deviation is a measure of how wide the scatter, or how large the variability, of the response parameter is. Minimizing the standard deviation will lead to a smaller range of variability; i.e., the chance that the response parameters will differ largely from the mean value decreases. Therefore, the goal of a Robust Design analysis is to minimize the standard deviation of a response parameter, as shown below.

• Kurtosis: Kurtosis is a measure of how peaked a distribution is. When kurtosis increases, the distribution is more peaked, and fewer samples will be located further away from the mean value. Therefore, the goal of a Robust Design analysis is to maximize the kurtosis of a response parameter, as shown below. You should read Guidelines and Best Practices before using kurtosis.

• Signal-to-Noise Ratios: The goal of minimizing the standard deviation (or noise) of a response parameter is inherently coupled with the goal of shifting the mean value (or signal). Different ratios are appropriate for different shifts of the mean (e.g., for maximizing the mean, minimizing the mean, etc.). The goal of a Robust Design analysis is to minimize the noise, which means the signal-to-noise ratio of a response parameter must be maximized. You should read Guidelines and Best Practices before using signal-to-noise ratios.

• Shannon Entropy: Shannon entropy is a measure of the complexity or predictability of the distribution of a response parameter. Entropy is a measure of the irreversible loss a real engineering system experiences as compared to a perfectly efficient, lossless system. For the distribution of a response parameter, entropy is a measure of the loss of information for a result subjected to uncertainty as compared to a completely predictable result. For example, if you knew that a response parameter always has a value of 5.0, regardless of the input parameter values, the response parameter would be completely predictable and very easy to describe, because a single scalar value sufficiently characterizes its behavior as a function of the input parameters. When the response parameter is affected by randomness, the predictability is lost and its behavior as a function of the input parameters is no longer characterized by a single value, but is more complex. The wider the scatter of the response parameter, the more predictability is lost and the more complex its behavior characterization. Therefore, the goal of a Robust Design analysis is to minimize the Shannon entropy of a response parameter.

• Six Sigma Analysis: Robust Design that is interpreted from a Six Sigma Analysis leads to an optimization problem that tries to achieve or enforce a design that satisfies Six Sigma Analysis quality goals, as outlined in Six Sigma Analysis. In this case, sigma levels (in probability and inverse probability tables) are used as Robust Design parameters. Depending on whether your focus is on the lower or upper specification limit, a Robust Design analysis will try to minimize the sigma level to below -6 or above +6, or both, as shown below. If +/- 6 is too strict (or not strict enough) for your study, you can adjust the value.

• Reliability-based Optimization: In a more general probabilistic sense, a product can be considered robust if it is reliable. If interpreted this way, Robust Design becomes an optimization tool to improve product reliability. Here, reliability is the probability that the product functions as expected; i.e., conforms to the specification criteria. This is very similar to Six Sigma Analysis, except that here you deal directly with the probabilities as parameters (in probability and inverse probability tables) in one of two ways:

• Insert the value of the lower or upper specification limit in the probability table. You will then obtain the probability of the response parameter dropping below that limit, which can be parameterized. Depending on whether it is the lower or upper limit, the analysis will try to either minimize or maximize the probability. See Guidelines and Best Practices for more details.

• Insert the targeted non-conformance probability into the inverse probability table. You will get a value for the response parameter corresponding to that non-conformance probability, which you can then parameterize. For a design that is not robust enough, the value will be outside the specified interval. Depending on whether it is the lower or upper limit, the analysis will try to either minimize or maximize the probability. See Guidelines and Best Practices for more details.