Individual and composite desirability

Assess how well a combination of input variables satisfies the goals you have defined for the responses. Individual desirability (d) evaluates how the settings optimize a single response; composite desirability (D) evaluates how the settings optimize a set of responses overall. Desirability has a range of zero to one. One represents the ideal case; zero indicates that one or more responses are outside their acceptable limits.

For example, a chemical engineer wants to maximize the yield of a chemical reaction by varying three input variables: reaction time, reaction temperature, and type of catalyst. At the same time, she wants to minimize cost, which is also affected by the three variables. Using the Response Optimizer, she defines target goals for yield and cost. Minitab calculates optimal settings for the input variables along with desirability values to indicate how well those settings achieve the response targets.

Yield = 44.8077    desirability = 0.98077

Cost = 28.0955     desirability = 0.87136

Composite Desirability = 0.9245

Here, the composite desirability (0.9245) is fairly close to 1, which indicates the settings appear to achieve favorable results for all responses as a whole. However, the individual desirability indicates that the settings are more effective at maximizing yield (0.98077) than at minimizing cost (0.87136). If minimizing cost is more important, the engineer may want to adjust the settings using an optimization plot, to achieve higher individual desirability for cost and lower individual desirability for yield.

Minitab's Response Optimizer calculates individual desirability using a desirability function (also called utility transfer function). You select a weight (from 0.1 to 10) to determine how much to emphasize reaching the target value. Composite desirability is the weighted geometric mean of the individual desirabilities for the responses. Minitab determines optimal settings for input variables by maximizing the composite desirability.