harrington1 {desire} | R Documentation |
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
.
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)
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. |
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)).
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
.
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.
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.
harrington2
for two sided Harrington type desirabilities
##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