optimum: Optimal factor settings

Description Usage Arguments Details Value Note Author(s) See Also Examples

View source: R/des_e.r

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

1
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.

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.

Value

optimum returns an object of class desOpt.

Note

For a example which shows the usage of optimum() in context please read the vignette for the package qualityTools at http://www.r-qualitytools.org/html/Improve.html.

Author(s)

Thomas Roth [email protected]

See Also

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

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
#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")

Example output

Loading required package: Rsolnp
Loading required package: MASS

Attaching package: 'qualityTools'

The following object is masked from 'package:stats':

    sigma

Warning messages:
1: In `[<-`(`*tmp*`, i, value = <S4 object of class "doeFactor">) :
  implicit list embedding of S4 objects is deprecated
2: In `[<-`(`*tmp*`, i, value = <S4 object of class "doeFactor">) :
  implicit list embedding of S4 objects is deprecated
3: In `[<-`(`*tmp*`, i, value = <S4 object of class "doeFactor">) :
  implicit list embedding of S4 objects is deprecated
Information about the factors:

           A       B       C
low      0.7      40     1.8
high     1.7      60     2.8
name  silica   silan  sulfur
unit                        
type numeric numeric numeric
-----------
   StandOrd RunOrder Block      A      B      C  y1   y2  y3   y4
5         1        1     1 -1.000 -1.000 -1.000 103  490 640 62.5
2         2        2     1  1.000 -1.000 -1.000 120  860 410 65.0
3         3        3     1 -1.000  1.000 -1.000 117  800 570 77.5
8         4        4     1  1.000  1.000 -1.000 139 1090 380 70.0
1         5        5     1 -1.000 -1.000  1.000 102  900 470 67.5
6         6        6     1  1.000 -1.000  1.000 132 1289 270 67.0
7         7        7     1 -1.000  1.000  1.000 132 1270 410 78.0
4         8        8     1  1.000  1.000  1.000 198 2294 240 74.5
9         9        9     1 -1.633  0.000  0.000 102  770 590 76.0
10       10       10     1  1.633  0.000  0.000 154 1690 260 70.0
11       11       11     1  0.000 -1.633  0.000  96  700 520 63.0
12       12       12     1  0.000  1.633  0.000 163 1540 380 75.0
13       13       13     1  0.000  0.000 -1.633 116 2184 520 65.0
14       14       14     1  0.000  0.000  1.633 153 1784 290 71.0
15       15       15     1  0.000  0.000  0.000 133 1300 380 70.0
16       16       16     1  0.000  0.000  0.000 133 1300 380 68.5
17       17       17     1  0.000  0.000  0.000 140 1145 430 68.0
18       18       18     1  0.000  0.000  0.000 142 1090 430 68.0
19       19       19     1  0.000  0.000  0.000 145 1260 390 69.0
20       20       20     1  0.000  0.000  0.000 142 1344 390 70.0
$y1
Target is to maximize y1 
lower Bound:  120 
higher Bound:  170 
Scale factor is:  1 1 
importance:  1 


$y2
Target is to maximize y2 
lower Bound:  1000 
higher Bound:  1300 
Scale factor is:  1 1 
importance:  1 


$y3
Target is  500  for y3 
lower Bound:  400 
higher Bound:  600 
Scale factor is: low = 1 and high = 1 
importance:  1 


$y4
Target is  67.5  for y4 
lower Bound:  60 
higher Bound:  75 
Scale factor is: low = 1 and high = 1 
importance:  1 



composite (overall) desirability: 0.583

            A      B      C
coded -0.0533  0.144 -0.872
real   1.1733 51.442  1.864

                    y1   y2      y3     y4
Responses      129.333 1300 466.397 67.997
Desirabilities   0.187    1   0.664  0.934

composite (overall) desirability: 0.58

        A      B      C
coded 0.0  0.136 -0.817
real  1.2 51.361  1.892

                    y1       y2      y3     y4
Responses      130.660 1299.669 456.937 67.980
Desirabilities   0.213    0.999   0.569  0.936

qualityTools documentation built on May 30, 2017, 1:43 a.m.