harrington2 {desire} | R Documentation |
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
.
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)
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. |
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).
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
.
Heike Trautmann trautmann@statistik.tu-dortmund.de, Detlef Steuer steuer@hsu-hamburg.de and Olaf Mersmann olafm@statistik.tu-dortmund.de
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.
harrington1
for one sided Harrington type desirabilities
##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)