SOAs

Creates stratum orthogonal arrays (also known as strong orthogonal arrays).

• Author: Ulrike Groemping, BHT Berlin.
• Contributor: Rob Carnell.

Actions	Coverage	Website

Installation

You can install the released version of SOAs from CRAN with:

install.packages("SOAs")

You can also install the development version of SOAs from here with:

if (!require(devtools)) install.packages("devtools")
devtools::install_github("bertcarnell/SOAs")

Details

This package constructs arrays in $s^{el}$ levels from orthogonal arrays in s levels. These are all based on equations of the type

$$D = s^{el-1} A_1 + ... + s A_{el-1} + A_{el},$$

or for $s^2$ levels,

$$D = s A + B$$

and for $s^3$ levels,

$$D = s^2 A + s B + C.$$

The constructions differ in how they obtain the ingredient matrices, and what properties can be guaranteed for the resulting D. Where a construction function guarantees orthogonal columns for all matrices D it produces, its name starts with a OSOA, otherwise with SOA.

If optimization is requested (default TRUE), space filling properties of D are improved using a level permutation algorithm by Weng (2014). This algorithm is applied for improving the phi_p criterion, which is often a reasonable surrogate for increasing the minimum distance.

Groemping (2023a) describes the constructions by He and Tang (2013, function SOAs), Liu and Liu (2015, function OSOAs_LiuLiu), He, Cheng and Tang (2018, function SOAs2plus_regular), Zhou and Tang (2019), Shi and Tang (2020, function SOAs_8level) and Li, Liu and Yang (2021) in unified notation. The constructions by Zhou and Tang (2019) and Li et al. (2021) are very close to each other and are both implemented in the three functions OSOAs, OSOAs_hadamard and OSOAs_regular.

Within the package, available SOA constructions for specific situations can be queried using the guide functions guide_SOAs and guide_SOAs_from_OA.

Besides the construction functions, properties of the resulting array D can be checked using the aforementioned function phi_p as well as check functions ocheck, ocheck3 for orthogonality and soacheck2D, soacheck3D for (O)SOA stratification properties, and Spattern for the space-filling pattern proposed by Tian and Xu (2022); the implementation of the latter will presumably become more important than the 2D and 3D check functions eventually.

There is one further construction, maximin distance level expansion (XiaoXuMDLE, MDLEs), that does not yield stratum (aka strong) orthogonal arrays and is available for comparison only (Xiao and Xu 2018).

References

Groemping, U. (2022). Implementation of the stratification pattern by Tian and Xu via power coding. Report 2022/03, Reports in Mathematics, Physics and Chemistry, Berliner Hochschule fuer Technik. `http://www1.bht-berlin.de/FB_II/reports/Report-2022-003.pdf`

Groemping, U. (2023a). A unifying implementation of stratum (aka strong) orthogonal arrays. Computational Statistics and Data Analysis 183, 1-28.

Groemping, U. (2023b). Implementating the stratification pattern for space-filling, with dimension by weight tables. Report 2023/01, Reports in Mathematics, Physics and Chemistry, Berliner Hochschule fuer Technik. `http://www1.bht-berlin.de/FB_II/reports/Report-2023-001.pdf`

He, Y., Cheng, C.S. and Tang, B. (2018). Strong orthogonal arrays of strength two plus. The Annals of Statistics 46, 457-468.

He, Y. and Tang, B. (2013). Strong orthogonal arrays and associated Latin hypercubes for computer experiments. Biometrika 100, 254-260.

Li, W., Liu, M.-Q. and Yang, J.-F. (2021). Construction of column-orthogonal strong orthogonal arrays. Statistical Papers .

Liu, H. and Liu, M.-Q. (2015). Column-orthogonal strong orthogonal arrays and sliced strong orthogonal arrays. Statistica Sinica 25, 1713-1734.

Shi, L. and Tang, B. (2020). Construction results for strong orthogonal arrays of strength three. Bernoulli 26, 418-431.

Tian, Y. and Xu, H. (2022). A minimum aberration-type criterion for selecting space-filling designs. Biometrika 109, 489-501.

Tian, Y. and Xu, H. (2023+). Stratification Pattern Enumerator and its Applications. To appear in J. Roy. Statist. Soc. Series B.

Weng, J. (2014). Maximin Strong Orthognal Arrays. Master’s thesis at Simon Fraser University under supervision of Boxin Tang and Jiguo Cao. https://summit.sfu.ca/item/14433

Xiao, Q. and Xu, H. (2018). Construction of Maximin Distance Designs via Level Permutation and Expansion. Statistica Sinica 28, 1395-1414.

Zhou, Y.D. and Tang, B. (2019). Column-orthogonal strong orthogonal arrays of strength two plus and three minus. Biometrika 106, 997-1004.