Derringer’s desirability functions

Jimidar, M., Bourguignon, B., and Massart, D. L. (1996). Application of Derringer s desirability function for the selection of optimum separation conditions in capillary zone electrophoresis. J. Chromatogr. A 740(1), 109-117. 

MCDM methods are applied when at least two responses need to be optimized simultaneously. Different approaches can be distinguished, for example, window programming, threshold approaches, utility functions. Derringer s desirability functions, Pareto optimality methods, Electre outranking relationships, and Promethee (7). In this chapter, only the Pareto optimality methods (7, 117, 118) and Derringer s desirability functions (7, 119, 120) will be discussed. 

A second MCDM approach is the use of Derringer s desirability functions. In this approach, all responses are transformed on the same scale and combined to one response, D, which then should be maximized. Each response is transformed on a scale between 0, representing the most undesirable outcome, and 1, representing the most desirable situation. The values of the transformed responses are called desirabilities. Different transformations are used, depend-... 

FIGURE 2.20. Derringer s desirability functions the response is optimal when (a) maximized, (b) minimized, and (c) at a given value. 

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