Generate Mixed-Level or Regular Fractional Factorial Designs

Description

generate_ff() constructs mixed-level fractional factorial designs or, when all factors share the same number of levels s, automatically searches for a regular s^{k-p} fractional factorial using generator relations.

#' The function performs:

• Part 1: Design construction (regular or mixed-level)

• Part 2: Design diagnostics: balance (Hhat), J2, GBM, alias chains, and strong confounding summary

• Part 3 (optional): Deterministic trend-free run order based on Coster (1993)

Output printing can be controlled via the parts argument.

Usage

generate_ff(
  levels_spec,
  n_runs,
  max_iter = 100,
  a = 1,
  b = 1,
  max_int_order = 3,
  alias_min_abs_corr = 0.9,
  tf = FALSE,
  parts = c(1, 2, 3),
  verbose = TRUE
)

Arguments

Details

Automatic Regular Fractional Factorial Detection

When all factors have the same number of levels s, and when n\_runs = s^{k-p}, the function attempts to find a regular s^{k-p} fraction via a heuristic generator search inspired by Guo et al. (2007). The objective minimized is:

The objective function minimized is Z = a * J2 + b * Hhat.

If no acceptable generator set is found, the algorithm reverts to a mixed-level design strategy.

Mixed-Level Fractional Factorials

Mixed-level designs are constructed using the Pantoja-Pacheco et al. (2021) NONBPA skeleton for nonmultiple levels, followed by a Guo-style coordinate exchange improvement on the Z-criterion.

Alias Structure (Rios-Lira et al., 2021)

Alias relationships are computed from the correlation matrix of the model matrix (main effects + interactions). Chains are built by selecting the pair of terms with the highest absolute correlation, choosing the lower-order term as the chain leader.

Trend-Free Run Order (Coster, 1993)

When tf = TRUE, a deterministic pairwise-swap algorithm produces a run order orthogonal to polynomial time trends (linear by default).

Value

A list containing:

• design_int -> integer-coded design

• design_labels -> decoded factor levels

• level_maps -> internal mapping of coded levels

• Hhat -> balance measure

• J2hat -> near-orthogonality measure

• GBM -> general balance metric

• gbm_resolution -> smallest order with imbalance

• model_matrix -> model matrix with interactions

• corr_matrix -> correlation matrix

• alias_chains -> alias chain structure

• alias_summary -> strong confounding pairs

• trend_free_result -> (if tf = TRUE) run order, reordered design, and final trend objective

Returned invisibly unless assigned.

References

Guo, Y., Simpson, J. R., & Pignatiello, J. J. (2007). Construction of Efficient Mixed-Level Fractional Factorial Designs. Journal of Quality Technology, 39(3), 241-257. doi:10.1080/00224065.2007.11917691

Pantoja-Pacheco, Y. V. et al. (2021). One Note for Fractionation and Increase for Mixed-Level Designs When the Levels Are Not Multiple. Mathematics, 9(13), 1455. doi:10.3390/math9131455

Rios-Lira, A. J. et al. (2021). Alias Structures and Sequential Experimentation for Mixed-Level Designs. Mathematics, 9(23), 3053. doi:10.3390/math9233053

Coster, D. C. (1993). Trend-Free Run Orders of Mixed-Level Fractional Factorial Designs. Annals of Statistics, 21(4), 2072-2086. doi:10.1214/aos/1176349410

Examples

# Mixed-level design (2 x 3 x 4), 12 runs, all parts printed
generate_ff(c(2,3,4), 12, tf = TRUE)

# Only Part 1 (design)
generate_ff(c(2,3,4), 12, parts = 1, tf = FALSE)

# Parts 1 and 2 only
generate_ff(c(2,3,4), 12, parts = c(1,2), tf = FALSE)

# Only Part 3 (trend-free run order)
generate_ff(c(2,3,4), 12, parts = 3, tf = TRUE)