One-sided Harrington type desirability function

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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

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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 y1 and y2 of variable Y with respective desirability values d1 and d2 determine the shape of the desirability function.

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

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##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