Two-sided Harrington type desirability function
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
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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)
vector of quantiles.
vector of probabilies.
number of observations.
two-sided Harrington type desirability function.
Lower Specification Limit of Y.
Upper Specification Limit of Y.
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.
vector of means.
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
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
dharrington2 give the density,
pharrington2 give the distribution function,
qharrington2 give the quantile function, and
rharrington2 generate random deviates.
the expected value and the variance of the desirability function for a
normally distributed random variable Y with
mean and sd(Y)=
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
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##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)
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