# Geometric Mean Desirability Index

### Description

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

### Usage

1 | ```
geometricDI(f, ..., weights)
``` |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
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)
``` |