Method - Response Optimization
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Minitab's Response Optimizer searches for a combination of input variables that jointly optimize a set of responses by satisfying the requirements for each response in the set. The optimization is accomplished by:

1    obtaining the individual desirability (d) for each response

2    combining the individual desirabilities to obtain the combined or composite desirability (D)

3    maximizing the composite desirability and identifying the optimal input variable settings

Obtaining individual desirability

First, Minitab obtains an individual desirability (d) for each response using the goals and boundaries that you have provided in the Setup dialog box. There are three goals to choose from. You may want to:

·    minimize the response (smaller is better)

·    target the response (target is best)

·    maximize the response (larger is better)

Suppose you have a response that you want to minimize. You need to determine a target value and an allowable maximum response value. The desirability for this response below the target value is one; above the maximum acceptable value the desirability is zero. The closer the response to the target, the closer the desirability is to one. The illustration below shows the default desirability function (also called utility transfer function) used to determine the individual desirability (d) for a "smaller is better" goal:

The shape of the desirability function between the upper bound and the target is determined by the choice of weight. The illustration above shows a function with a weight of one. To see how changing a weight affects the shape of the desirability function, see Setting the weight for the desirability function.

Obtaining the composite desirability

After Minitab calculates an individual desirability for each response, they are combined to provide a measure of the composite, or overall, desirability of the multi-response system. This measure of composite desirability (D) is the weighted geometric mean of the individual desirabilities for the responses. The individual desirabilities are weighted according to the importance that you assign each response. For a discussion, see Specifying the importance for composite desirability.

Maximizing the composite desirability

Finally, Minitab employs a reduced gradient algorithm with multiple starting points that maximizes the composite desirability to determine the numerical optimal solution (optimal input variable settings).

More    You may want to fine tune the solution by adjusting the input variable settings using the interactive optimization plot. See Using the optimization plot.