harrington2 {desire}R Documentation

Two-sided Harrington type desirability function

Description

Returns a two sided desirability function of the Harrington type. Density, distribution function, quantile function and random number generation for the distribution of the two-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

harrington2(LSL, USL, n)
## S3 method for class 'harrington2':
ddesire(x, f, mean, sd)
## S3 method for class 'harrington2':
pdesire(q, f, mean, sd)
## S3 method for class 'harrington2':
qdesire(p, f, mean, sd)
dharrington2(x, LSL, USL, n, mean, sd)
pharrington2(q, LSL, USL, n, mean, sd)
qharrington2(p, LSL, USL, n, mean, sd)
rharrington2(ns, LSL, USL, n, mean, sd)
eharrington2(LSL, USL, n, mean, sd)
vharrington2(LSL, USL, n, mean, sd)

Arguments

x,q vector of quantiles.
p vector of probabilies.
ns number of observations.
f two-sided Harrington type desirability function.
LSL Lower Specification Limit of Y.
USL Upper Specification Limit of Y.
n Kurtosis parameter of desirability function. Values > 1 result in smoother shapes around the target value T = (LSL+USL)/2. Values < 1 already penalize small target deviations.
mean vector of means.
sd vector of standard deviations.

Details

harrington2(LSL, USL, n) is the two-sided desirability function of Harrington type (Harrington (1965)). It aims at the specification of desired values of a variable Y which has to be optimized regarding a target value T. Y is transformed onto a unitless scale to the interval [0,1]. LSL and USL are associated with a desirability of 1/e., approx. 0.37. LSL and USL have to be chosen symmetrically around the target value T.

The density and distribution functions of Harrington's two-sided desirability function d given a normally distributed variable Y with E(Y)= mean and sd(Y)=sd can be determined analytically, see Trautmann and Weihs (2006).

Value

harrington2(LSL, USL, n) returns a function object of the two-sided desirability function of the Harrington type (see example below).
ddesire / dharrington2 give the density, pdesire / pharrington2 give the distribution function, qdesire / qharrington2 give the quantile function, and rdesire / rharrington2 generate random deviates. edesire / eharrington2 and vdesire / vharrington2 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.

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 for one sided Harrington type desirabilities

Examples

##Assigning the function object to h: 
h <- harrington2(3,7,1) 

## Plot of desirability function: 
plot(h)

## Desirability function of a vector: 
h(seq(2,8,0.1))

## d/p/q/r/e/v examples: 
ddesire(4, h, 0, 1)
dharrington2(4, 3, 7, 1, 0, 1) 

ddesire(4, h, c(0,0.5),c(1,1.5))

pdesire(4, h, 0, 1)
pharrington2(4, 3, 7, 1, 0, 1)

qdesire(0.8, h, 0, 1)
qharrington2(0.8, 3, 7, 1, 0, 1)

rdesire(1e6, h, 0, 1)
rharrington2(1e6, 3, 7, 1, 0, 1)

edesire(h,3,0.5)

vdesire(h,3,0.5)

[Package desire version 1.0.5 Index]