# One-sided Harrington type desirability function

### Description

Returns a one-sided desirability function of the Harrington type.
Density, distribution function, quantile function and random number
generation for the distribution of the one-sided Harrington
desirability function are computed given a normally distributed
variable *Y* with expected value equal to `mean`

and standard
deviation equal to `sd`

.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ```
harrington1(y1, d1, y2, d2)
## S3 method for class 'harrington1'
ddesire(x, f, mean, sd)
## S3 method for class 'harrington1'
pdesire(q, f, mean, sd)
## S3 method for class 'harrington1'
qdesire(p, f, mean, sd)
## S3 method for class 'harrington1'
edesire(f, mean, sd)
## S3 method for class 'harrington1'
vdesire(f, mean, sd)
dharrington1(x, y1, d1, y2, d2, mean, sd)
pharrington1(q, y1, d1, y2, d2, mean, sd)
qharrington1(p, y1, d1, y2, d2, mean, sd)
rharrington1(n, y1, d1, y2, d2, mean, sd)
eharrington1(y1, d1, y2, d2, mean, sd)
vharrington1(y1, d1, y2, d2, mean, sd)
``` |

### Arguments

`x,q` |
vector of quantiles. |

`p` |
vector of probabilies. |

`n` |
number of observations. |

`f` |
one-sided Harrington type desirability function. |

`y1,d1,y2,d2` |
Two values |

`mean` |
vector of expected values of normal distributions. |

`sd` |
vector of standard deviations of normal distributions. |

### Details

`harrington1(y1, d1, y2, d2)`

is the one-sided desirability
function of Harrington type (Harrington (1965)). It aims at the
specification of desired values of a variable *Y* which has to be
minimized or maximized. *Y* is transformed onto a unitless scale
to the interval [0,1].

Harrington's one-sided desirability function `d`

given a normally
distributed variable *Y* with *E(Y)=* `mean`

and
*sd(Y)=*`sd`

has the Double Lognormal Distribution (Holland
and Ahsanullah (1989)).

### Value

`harrington1(y1, d1, y2, d2)`

returns a function object of the
one-sided desirability function of the Harrington type (see example
below). Values *b_0* and *b_1* of the desirability function
formula are determined.

`ddesire`

/`dharrington1`

give the density, `pdesire`

/
`pharrington1`

give the distribution function, `qdesire`

/
`qharrington1`

give the quantile function, and `rdesire`

/
`rharrington1`

generate random deviates.
`edesire`

/ `eharrington1`

and `vdesire`

/
`vharrington1`

compute the expected value and the variance of the
desirability function for a normally distributed random variable
*Y* with *E(Y)=*`mean`

and *sd(Y)=*`sd`

.

### 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.

B. Holland, M. Ahsanullah (1989): Further Results on the Distribution of Meinhold and Singpurwalla.
*The American Statistician* **43** (4): 216-219.

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

### See Also

`harrington2`

for two sided Harrington type desirabilities

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | ```
##Assigning the function object to h:
h <- harrington1(-2, .1, 2, .9)
## Plot of desirability function:
plot(h)
## Desirability function of a vector:
h(seq(-2,2,0.1))
## d/p/q/r/e/v examples:
ddesire(.8, h, 0, 1)
dharrington1(.8, -2, .1, 2, .9, 0, 1)
ddesire(.8, h, c(0,0.5), c(1,1.5))
pdesire(.8, h, 0, 1)
pharrington1(.8, -2, .1, 2, .9, 0, 1)
qdesire(.8, h, 0, 1)
qharrington1(.8, -2, .1, 2, .9, 0, 1)
rdesire(1e6, h, 0, 1)
rharrington1(1e6, -2, .1, 2, .9, 0, 1)
edesire(h,3,0.5)
eharrington1(-2, .1, 2, .9,3,0.5)
vdesire(h,3,0.5)
vharrington1(-2, .1, 2, .9,3,0.5)
## b_0 and b_1 values:
environment(h)$b0
environment(h)$b1
``` |