Geometric Mean Desirability Index

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Description

Computes the weighted geometric mean of a number of desirability functions.

Usage

1

Arguments

f, ...

desirability functions

weights

vector of weights

Details

The Desirability Index was introduced by Harrington (1965), and the concept was extended by Derringer and Suich (1980). It is a means for multicriteria (quality) optimization in industrial quality management. All desirability functions of the quality criteria are combined into a univariate global quality criterion in [0,1] which has to be optimized.

The function can be used for Harrington as well as Derringer and Suich desirability functions.

Value

geometricDI(f, ..., weights) returns a function object of the Geometric Mean Desirability Index.

Author(s)

Heike Trautmann trautmann@statistik.tu-dortmund.de, Detlef Steuer steuer@hsu-hamburg.de and Olaf Mersmann olafm@statistik.tu-dortmund.de

References

J. Harrington (1965): The desirability function. Industrial Quality Control, 21: 494-498.

G.C. Derringer, D. Suich (1980): Simultaneous optimization of several response variables. Journal of Quality Technology 12 (4): 214-219.

D. Steuer (2005): Statistische Eigenschaften der Multikriteriellen Optimierung mittels Wuenschbarkeiten. Dissertation, Dortmund University of Technology, http://hdl.handle.net/2003/20171.

H. Trautmann, C. Weihs (2006): On the Distribution of the Desirability Index using Harrington's Desirability Function. Metrika 63(2): 207-213.

See Also

harrington1 and harrington2 for Harrington type desirability functions; derringerSuich for desirability functions of Derringer and Suich; minimumDI,meanDI for other types of Desirability indices.

Examples

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h1 <- harrington1(-2, .9, 2, .1)
h2 <- harrington2(0, 2, 2)

di <- geometricDI(h1, h2, weights=c(1/3, 2/3))
di(c(0, 1))

## Desirability Index of vector input:
h <- harrington2(3,7,1)
g <- harrington1(-2, .1, 2, .9) 

d <- geometricDI(h, g, weights=c(0.5, 0.5))

m <- matrix(c(seq(2, 8, 0.1), seq(-2, 4, 0.1)), ncol=2, byrow=FALSE)
apply(m, 1, d)