Derringer’s desirability

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. 

To illustrate the apphcation of the Derringer and Suich method, we are going to make a small adaptation of the problem with three factors and two responses presented in Section 6.3. We start with the data in Table 6.9, but initially suppose that we are interested in obtaining a product with a value of Young s modulus as close as possible to 2.0 MPa, and also that we want a yield not much lower than 15%. The algorithm we used (StatSoft, 2004) requires specification of the numerical values of L, U and T, besides s, t and the desirabilities. To arrive at the results we present next, we used the values shown in Table 6.12. 

---