Desirability Function

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Description

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

Usage

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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 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

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#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)

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