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## harrington2.R - Two sided Harrington type desiraility functions
##
## Authors:
## Heike Trautmann <trautmann@statistik.tu-dortmund.de>
## Detlef Steuer <detlef.steuer@hsu-hamburg.de>
## Olaf Mersmann <olafm@statistik.tu-dortmund.de>
##
harrington2 <- function(LSL, USL, n) {
ev <- function(y, ...) {
ys <- (2*y - s)/d
return(exp(-abs(ys)^n))
}
if (USL <= LSL)
stop("LSL must be smaller than USL.")
if (n <= 0)
stop("Invalid exponent 'n'")
## Precompute:
s <- USL + LSL
d <- USL - LSL
class(ev) <- c("harrington2", "desire.function")
attr(ev, "desire.type") <- "Two sided Harrington"
attr(ev, "y.range") <- c(LSL-d, USL + d)
return(ev)
}
## Print function
print.harrington2 <- function(x, ...) {
e <- environment(x)
message(" Two sided Harrington type desirability")
message("")
p <- c(e$LSL, e$USL, e$n)
names(p) <- c("LSL", "USL", "n")
message("Parameters:")
print.default(format(p, width=8), print.gap=2, quote=FALSE, ...)
}
## Plot function
plot.harrington2 <- function(x, ...) {
e <- environment(x)
plot.desire.function(x, ...)
abline(v=c(e$LSL, e$USL), col="grey", lty=2)
mtext(c("LSL", "USL"), at=c(e$LSL, e$USL), line=.5)
}
## Density:
dharrington2 <- function(x, LSL, USL, n, mean, sd) {
s <- USL + LSL
d <- USL - LSL
n0 <- 1/n
n1 <- n0 - 1
mu.t <- (2/d) * mean - s / d
sd.t <- (2/d) * sd
c0 <- sqrt(2*pi) * sd.t * x * n
c1 <- -log(x)
c1a <- c1^n0
c1b <- c1^n1
c2 <- 2*sd.t^2
c3 <- (c1a - mu.t)^2 / c2
c4 <- (c1a + mu.t)^2 / c2
r <- c1b/c0 * (exp(-c3) + exp(-c4))
return(r)
}
ddesire.harrington2 <- function(x, f, mean, sd) {
e <- environment(f)
dharrington2(x, e$LSL, e$USL, e$n, mean, sd)
}
## CDF
pharrington2 <- function(q, LSL, USL, n, mean, sd) {
s <- USL + LSL
d <- USL - LSL
mu.t <- 2 / d * mean - s / d
sd.t <- (2 / d) * sd
n0 <- 1/n
c1 <- -log(q)^n0
return(2 - pnorm((c1 - mu.t)/sd.t) - pnorm((c1 + mu.t)/sd.t))
}
pdesire.harrington2 <- function(q, f, mean, sd) {
e <- environment(f)
pharrington2(q, e$LSL, e$USL, e$n, mean, sd)
}
## Quantiles
qharrington2 <- function(p, LSL, USL, n, mean, sd) {
f <- function(q)
(p - pharrington2(q, LSL, USL, n, mean, sd))^2
## FIXME: Ugly search
optimize(f, c(0, 1))$minimum
}
qdesire.harrington2 <- function(p, f, mean, sd) {
e <- environment(f)
qharrington2(p, e$LSL, e$USL, e$n, mean, sd)
}
## Random numbers
rharrington2 <- function(ns, LSL, USL, n, mean, sd)
harrington2(LSL, USL, n)(rnorm(ns, mean, sd))
## Expectation
eharrington2 <- function(LSL, USL, n, mean, sd)
stop("Not implemented")
## Variance
vharrington2 <- function(LSL, USL, n, mean, sd)
stop("Not implemented")
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