qualityTools (version 1.31.1)

optimum: Optimal factor settings

Description

Calculates the best factors settings with regard to defined desirabilities and constraints. Two approaches are currently supported, (I) evaluating (all) possible factor settings and (II) using the function optim. Using optim optim initial values for the factors to be optimized over can be set via start.

Usage

optimum(fdo, constraints, steps = 25, type = "grid", start, ...)

Arguments

fdo

an object of class facDesign with fits and fits set

constraints

constraints for the factors such as list(A = c(-2,1), B = c(0, 0.8))

steps

number of grid points per factor if type = "grid"

type

type of search "grid" or "optim" see DESCRIPTION

start

initial values for the factors to be optimized over.

...

Value

• an object of class desOpt

Details

start should be defined in cases where type = "optim" fails to calculate the best factor setting

References

see optim

See Also

optim

Examples

#BEWARE BIG EXAMPLE --Simultaneous Optimization of Several Response Variables--
#Source: DERRINGER, George; SUICH, Ronald: Simultaneous Optimization of Several Response Variables. Journal of Quality Technology Vol. 12, No. 4, p. 214-219

#Define the response suface design as given in the paper and sort via Standard Order
fdo = rsmDesign(k = 3, alpha = 1.633, cc = 0, cs = 6)
fdo = randomize(fdo, so = TRUE)

#Attaching the 4 responses
y1 = c(102,120,117,198,103,132,132,139,102,154,96,163,116,153,133,133,140,142,145,142)
y2 = c(900,860,800,2294,490,1289,1270,1090,770,1690,700,1540,2184,1784,1300,1300,1145,1090,1260,1344)
y3 = c(470,410,570,240,640,270,410,380,590,260,520,380,520,290,380,380,430,430,390,390)
y4 = c(67.5,65,77.5,74.5,62.5,67,78,70,76 ,70,63 ,75,65,71 ,70,68.5,68,68,69,70)
response(fdo) = data.frame(y1, y2, y3, y4)[c(5,2,3,8,1,6,7,4,9:20),]

#setting names and real values of the factors
names(fdo) = c("silica", "silan", "sulfur")
highs(fdo) = c(1.7, 60, 2.8)
lows(fdo) = c(0.7, 40, 1.8)

#summary of the response surface design
summary(fdo)

#setting the desires
desires(fdo) = desirability(y1, 120, 170, scale = c(1,1), target = "max")
desires(fdo) = desirability(y2, 1000, 1300, target = "max")
desires(fdo) = desirability(y3, 400, 600, target = 500)
desires(fdo) = desirability(y4, 60, 75, target = 67.5)
desires(fdo)

#Have a look at some contourPlots
par(mfrow = c(2,2))
contourPlot(A, B, y1, data = fdo)
contourPlot(A, B, y2, data = fdo)
wirePlot(A, B, y1, data = fdo)
wirePlot(A, B, y2, data = fdo)


#setting the fits as in the paper
fits(fdo) = lm(y1 ~ A + B + C + A:B + A:C + B:C + I(A^2) + I(B^2) + I(C^2), data = fdo)
fits(fdo) = lm(y2 ~ A + B + C + A:B + A:C + B:C + I(A^2) + I(B^2) + I(C^2), data = fdo)
fits(fdo) = lm(y3 ~ A + B + C + A:B + A:C + B:C + I(A^2) + I(B^2) + I(C^2), data = fdo)
fits(fdo) = lm(y4 ~ A + B + C + A:B + A:C + B:C + I(A^2) + I(B^2) + I(C^2), data = fdo)
#fits(fdo)

#calculate the same best factor settings as in the paper using type = "optim"
optimum(fdo, type = "optim")

#calculate (nearly) the same best factor settings as in the paper using type = "grid"
optimum(fdo, type = "grid")