# Desirability Function

### Description

Creates desirability functions for use in the optimization of multiple responses.

### Usage

1 2 | ```
desirability(response, low, high, target = "max", scale = c(1, 1),
importance = 1, constraints)
``` |

### Arguments

`response` |
name of the response. |

`low` |
lowest acceptable value for the response. |

`high` |
highest acceptable value for the response. |

`target` |
desired target value of the response. |

`scale` |
numeric value giving the scaling factors for one and two sided transformations. |

`importance` |
a value ranging from 0.1 to 10, used to calculate a weighted importance i.e. with importances 1,2 and 4 D=[(d1)^1,(d2)^2,(d3)^4]^(1/7). |

`constraints` |
not yet implemented. |

### Details

For a product to be developed different values of responses are desired leading to multiple response optimization. Minimization, Maximization as well as a specific target value are defined using desirability functions. A desirability function tranforms the values of a response into [0,1] where 0 stands for a non acceptable value of the response and 1 for values where higher/lower (depending on the direction of the optimization) values of the response have little merit.

A first desirability function was specified by Harrington (1965), Derringer and Suich (1980) came up with a modified appproach to transform several responses into a desirability function which was extended with the possibility of specifying weights Derringer (1994). Castillo, Montgomery and McCarville came up with a another modification. The first and the latter are not implemented!

### Value

This function returns a desirability function.

### Note

For an example in context which shows the usage of the function `desirability()`

please read the vignette for the package `qualityTools`

at http://www.r-qualitytools.org/html/Improve.html.

### Author(s)

Thomas Roth thomas.roth@tu-berlin.de

### References

HARRINGTON, E.C.:'The Desirability Function', Journal of the American Society for Quality Control, pp. 494-498, 1965.

DERRINGER, G.; SUICH, R. 'Simulaneous Optimization of Several Response Variables', Journal of Quality Technology, vol. 12, no. 4. 214-219, 1980.

DERRINGER, G.: 'A Balancing Act: Optimizing a Product's Properties', Quality Progress, vol. 27, no. 6, pp. 51-58, 1994.

CASTILLO; MONTGOMERY; MCCARVILLE: 'Modified Desirability Functions for Multiple Response Optimization', Journal of Quality Technology, vol. 28, no. 3, pp. 337-345, 1996.

### See Also

`desires`

`optimum`

http://www.r-qualitytools.org/html/Improve.html

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
#Maximization of a response
#define a desirability for response y where higher values of y are better
#as long as the response is smaller than high
d = desirability(y, low = 6, high = 18, target = "max")
#show and plot the desirability function
d; plot(d)
#Minimization of a response including a scaling factor
#define a desirability for response y where lower values of y are better
#as long as the response is higher than low
d = desirability(y, low = 6, high = 18, scale = c(2),target = "min")
#show and plot the desirability function
d; plot(d)
#Specific target of a response is best including a scaling factor
#define a desirability for response y where desired value is at 8
#and values lower than 6 as well as values higher than 18 are not acceptable
d = desirability(y, low = 6, high = 18, scale = c(0.5,2),target = 12)
#show and plot the desirability function
d; plot(d)
``` |