# desirability: Desirability Function In qualityTools: Statistical Methods for Quality Science

## 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. `target` can be “max”,“min” or any specefic numeric value. `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 [email protected]

## 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.

`desires`
`optimum`
 ``` 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) ```