qualityTools (version 1.53)

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 or gosolnp of the Rsolnp package. Using optim optim initial values for the factors to be optimized over can be set via start. The optimality of the solution depends critically on the starting parameters which is why it is recommended to use type="gosolnp" although calculation takes a while.

Usage

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

Arguments

fdo

an object of class facDesign with fits and desires 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,optim or gosolnp are supported (see DESCRIPTION).

start

numerical vector giving the initial values for the factors to be optimized over.

...

further aguments.

Value

• optimum returns an object of class desOpt.

Details

It is recommened to use type="gosolnp". Derringer and Suich (1994) desirabilities do not have continuous first derivatives, more precisely they have points where their derivatives do not exist, start should be defined in cases where type = "optim" fails to calculate the best factor setting.

See Also

optim desirability desires gosolnp http://www.r-qualitytools.org/Improve.html

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")