desire (version 1.0.7)

harrington2: 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)
"ddesire"(x, f, mean, sd)
"pdesire"(q, f, mean, sd)
"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.

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.

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).

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

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)