steepAscent: Steepest Ascent
In qualityTools: Statistical Methods for Quality Science

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

steepAscent is a method to calculate the steepest ascent for a facDesign object.

1	steepAscent(factors, response, size = 0.2, steps = 5, data)

`factors`	list containing vector of factor names (coded) to be included in calculation, first factor is the reference factor.
`response`	character - response given in data.
`size`	numeric integer value giving the step size in coded units for the first factor given in factors. By default `size` is set to ‘0.2’.
`steps`	numeric integer value giving the number of steps. By default `step` is set to ‘5’.
`data`	needs to be an object of class `facDesign`.

A first order model is fitted for the factors given in factors. Based on the step size given the steepest ascent is calculated.

steepAscent returns an object of class steepAscent.

This is the steepest ascent for a single response considering main effects only.
For an example in context which shows the usage of the function steepAscent() to an object of class facDesign, please read the vignette for the package qualityTools at http://www.r-qualitytools.org/html/Improve.html.

Thomas Roth thomas.roth@tu-berlin.de

http://www.itl.nist.gov/div898/handbook/pri/section5/pri5311.htm

desires for multiple response optimization usign desirabilities
http://www.r-qualitytools.org/html/Improve.html

#Example from References
fdo = facDesign(k = 2, centerCube = 5)
lows(fdo) = c(170, 150)
highs(fdo) = c(230, 250)
names(fdo) = c("temperature", "time")
units(fdo) = c("C", "minutes")
yield = c(32.79, 24.07, 48.94, 52.49, 38.89, 48.29, 29.68, 46.5, 44.15)
response(fdo) = yield
summary(fdo)

sao = steepAscent(factors = c("B", "A"), response = "yield", size = 1,
                  data = fdo)
sao
obs.yield = c(NA, 56.2, 71.49, 75.63, 72.31, 72.10)
response(sao) = obs.yield
plot(sao, type = "b", col = 2, main = "Steepest Ascent")

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
Information about the factors:

               A       B
low          170     150
high         230     250
name temperature    time
unit           C minutes
type     numeric numeric
-----------
  StandOrd RunOrder Block  A  B yield
4        4        1     1  1  1 32.79
3        3        2     1 -1  1 24.07
2        2        3     1  1 -1 48.94
5        5        4     1  0  0 52.49
9        9        5     1  0  0 38.89
6        6        6     1  0  0 48.29
7        7        7     1  0  0 29.68
8        8        8     1  0  0 46.50
1        1        9     1 -1 -1 44.15

Steepest Ascent for fdo 

  Run Delta B.coded A.coded B.real A.real
1   1     0       0   0.000    200    200
2   2     1      -1   0.373    150    211
3   3     2      -2   0.746    100    222
4   4     3      -3   1.119     50    234
5   5     4      -4   1.492      0    245
6   6     5      -5   1.864    -50    256
  Run Delta B.coded   A.coded B.real   A.real "yield"
1   1     0       0 0.0000000    200 200.0000      NA
2   2     1      -1 0.3728954    150 211.1869      NA
3   3     2      -2 0.7457908    100 222.3737      NA
4   4     3      -3 1.1186862     50 233.5606      NA
5   5     4      -4 1.4915816      0 244.7474      NA
6   6     5      -5 1.8644770    -50 255.9343      NA