Robustification

Robustification is a form of optimisation whereby a system is made less sensitive to the effects of random variability, or noise, that is present in that system’s input variables and parameters. The process is typically associated with engineering systems, but the process can also be applied to a political policy, a business strategy or any other system that is subject to the effects of random variability.

Robustification as it is defined here is sometimes referred to as parameter design or robust parameter design (RPD) and is often associated with Taguchi methods. Within that context, robustification can include the process of finding the inputs that contribute most to the random variability in the output and controlling them, or tolerance design. At times the terms design for quality or Design for Six Sigma (DFSS) might also be used as synonyms.

Robustification works by taking advantage of two different principles.

Consider the graph below of a relationship between an input variable x and the output Y, for which it is desired that a value of 7 is taken, of a system of interest. It can be seen that there are two possible values that x can take, 5 and 30. If the tolerance for x is independent of the nominal value, then it can also be seen that when x is set equal to 30, the expected variation of Y is less than if x were set equal to 5. The reason is that the gradient at x = 30 is less than at x = 5, and the random variability in x is suppressed as it flows to Y.

This basic principle underlies all robustification, but in practice there are typically a number of inputs and it is the suitable point with the lowest gradient on a multi-dimensional surface that must be found.

Consider a case where an output Z is a function of two inputs x and y that are multiplied by each other.

Z = x y

For any target value of Z there is an infinite number of combinations for the nominal values of x and y that will be suitable. However, if the standard deviation of x was proportional to the nominal value and the standard deviation of y was constant, then x would be reduced (to limit the random variability that will flow from the right hand side of the equation to the left hand side) and y would be increased (with no expected increase random variability because the standard deviation is constant) to bring the value of Z to the target value. By doing this, Z would have the desired nominal value and it would be expected that its standard deviation would be at a minimum: robustified.

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Wikipedia