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

This function looks at all combinations of specified design parameters
for central-composite designs, calculates other quantities such as
the `alpha`

values for rotatability and orthogonal blocking, imposes
specified restrictions, and outputs the best combinations in a specified order.
This serves as an aid in identifying good designs. The design itself can
then be generated using `ccd`

, or in pieces using `cube`

, `star`

, etc.

1 2 3 |

`k` |
Number of factors in the design |

`n.c` |
Number(s) of factorial points in each cube block |

`n0.c` |
Numbers(s) of center points in each cube block |

`blks.c` |
Number(s) of cube blocks that together comprise one rep of the cube portion |

`n0.s` |
Numbers(s) of center points in each star (axis-point) block |

`bbr.c` |
Number(s) of copies of each cube block |

`wbr.s` |
Number(s) of replications of each star poit within a block |

`bbr.s` |
Number(s) of copies of each star block |

`best` |
How many designs to list. Use |

`sortby` |
String(s) containing numeric expressions that are each evaluated and used as sorting key(s).
Specify |

`restrict` |
Optional string(s) containing Boolean expressions that are each evaluated. Only combinations where all
expressions are |

A grid is created with all combinations of `n.c`

, `n0.c`

, ..., `bbr.s`

.
Then for each row of the grid, several additional variables
are computed:

`n.s`

The total number of axis points in each star block

`N`

The total number of observations in the design

`alpha.rot`

The position of axis points that make the design rotatable. Rotatability is achieved when design moment [iiii] = 3[iijj] for i and j unequal.

`alpha.orth`

The position of axis points that make the blocks mutually orthogonal. This is achieved when design moments [ii] within each block are proprtional to the number of observations within the block.

`agreement`

The absolute value of the log of the ratio of

`alpha.rot`

and`alpha.orth`

. This measures agreement between the two`alpha`

s.

If `restrict`

is provided, only the cases where the expressions are all `TRUE`

are kept.
(Regardless of `restrict`

, rows are eliminated where there are
insufficient degrees of freedom to estimate all needed effects for a
second-order model.)
The rows are
sorted according to the expressions in `sortby`

; the default is to sort
by `agreement`

and `N`

, which is suitable for finding designs
that are both rotatable and orthogonally blocked.

A `data.frame`

containing `best`

or fewer rows, and variables
`n.c`

, `n0.c`

, `blks.c`

, `n.s`

, `n0.s`

, `bbr.c`

,
`wbr.s`

, `bbr.s`

, `N`

, `alpha.rot`

, and `alpha.orth`

,
as described above.

Russell V. Lenth

Lenth RV (2009) “Response-Surface Methods in R, Using rsm”,
*Journal of Statistical Software*, 32(7), 1–17.
doi: 10.18637/jss.v032.i07

Myers, RH, Montgomery, DC, and Anderson-Cook, CM (2009)
*Response Surface Methodology* (3rd ed.), Wiley.

1 2 3 4 5 6 7 8 9 10 11 | ```
library(rsm)
### List CCDs in 3 factors with between 10 and 14 runs per block
ccd.pick(3, n0.c=2:6, n0.s=2:8)
# (Generate the design that is listed first:)
# ccd(3, n0=c(6,4))
### Find designs in 5 factors containing 1, 2, or 4 cube blocks
### of 8 or 16 runs, 1 or 2 reps of each axis point,
### and no more than 70 runs altogether
ccd.pick(5, n.c=c(8,16), blks.c=c(1,2,4), wbr.s=1:2, restrict="N<=70")
``` |

```
n.c n0.c blks.c n.s n0.s bbr.c wbr.s bbr.s N alpha.rot alpha.orth
1 8 6 1 6 4 1 1 1 24 1.681793 1.690309
2 8 5 1 6 3 1 1 1 22 1.681793 1.664101
3 8 3 1 6 2 1 1 1 19 1.681793 1.705606
4 8 4 1 6 2 1 1 1 20 1.681793 1.632993
5 8 4 1 6 3 1 1 1 21 1.681793 1.732051
6 8 5 1 6 4 1 1 1 23 1.681793 1.754116
7 8 6 1 6 3 1 1 1 23 1.681793 1.603567
8 8 6 1 6 5 1 1 1 25 1.681793 1.772811
9 8 2 1 6 2 1 1 1 18 1.681793 1.788854
10 8 5 1 6 2 1 1 1 21 1.681793 1.568929
n.c n0.c blks.c n.s n0.s bbr.c wbr.s bbr.s N alpha.rot alpha.orth
1 16 6 1 10 1 1 1 1 33 2.000000 2.000000
2 16 8 1 10 2 1 1 1 36 2.000000 2.000000
3 16 10 1 10 3 1 1 1 39 2.000000 2.000000
4 16 5 2 20 1 1 2 1 63 2.000000 2.000000
5 16 6 2 20 2 1 2 1 66 2.000000 2.000000
6 8 3 4 20 2 1 2 1 66 2.000000 2.000000
7 16 7 2 20 3 1 2 1 69 2.000000 2.000000
8 16 8 2 10 7 1 1 1 65 2.378414 2.380476
9 8 4 4 10 7 1 1 1 65 2.378414 2.380476
10 16 1 2 10 2 1 1 1 46 2.378414 2.376354
```

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