Advertisement

An Evaluation of Estimation Capacity Under the Conditional Main Effect Parameterization

  • Arman SabbaghiEmail author
Original Article
  • 47 Downloads
Part of the following topical collections:
  1. Algorithms, Analysis and Advanced Methodologies in the Design of Experiments

Abstract

The conditional main effect (CME) parameterization system can enable more informative analyses of regular two-level fractional factorial designs compared to the traditional orthogonal components system. However, formal evaluations of estimation capacities for designs under CME models have yet to be performed. We establish a necessary and sufficient condition for a model consisting of all of the main effects and a selection of CMEs to be estimable in a regular two-level design of resolution at least III. Our condition illuminates the implications of the maximum estimation capacity criterion for analyses of such traditional and conditional effects. A novel aspect of our evaluations is the direct derivation of D-efficiencies for regular designs of resolution at least III with respect to CME models in which the selected CMEs are not siblings or family members, and their corresponding two-factor interactions are not completely aliased with a main effect.

Keywords

Complex aliasing Experimental design Partial aliasing Regular fractional factorial design 

Mathematics Subject Classification

62K15 05B15 

Notes

Acknowledgements

We are grateful to two reviewers for many valuable comments that improved this paper. We also thank the participants of the 2018 International Conference on Advances in Interdisciplinary Statistics and Combinatorics (AISC 2018), especially Robert Mee, J.P. Morgan, and Min Yang, for their insightful discussions that motivated the investigation in this paper.

Compliance with Ethical Standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

References

  1. 1.
    Box GEP, Hunter JS (1961) The \(2^{k-p}\) fractional factorial designs. Technometrics 3:311–352MathSciNetzbMATHGoogle Scholar
  2. 2.
    Cheng CS (2014) Theory of factorial design: single- and multi-stratum experiments. Monographs on statistics and applied probability, 1st edn. CRC Press, Boca RatonGoogle Scholar
  3. 3.
    Finney DJ (1945) The fractional replication of factorial experiments. Ann Eugen 12:291–301CrossRefGoogle Scholar
  4. 4.
    Fontana R, Pistone G, Rogantin MP (2000) Classification of two-level factorial fractions. J Stat Plan Inference 87(1):149–172MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fries A, Hunter WG (1980) Minimum aberration \(2^{k-p}\) designs. Technometrics 2:601–608zbMATHGoogle Scholar
  6. 6.
    Hamada MS, Wu CFJ (1992) Analysis of designed experiments with complex aliasing. J Qual Technol 24(3):130–137CrossRefGoogle Scholar
  7. 7.
    Mak S, Wu CFJ (2019) cmenet: a new method for bi-level variable selection of conditional main effects. J Am Stat Assoc 114(526):844–856MathSciNetCrossRefGoogle Scholar
  8. 8.
    Mason RL, Gunst RF, Hess JL (2003) Statistical design and analysis of experiments: with applications to engineering and science. Wiley series in probability and statistics, 2nd edn. Wiley, HobokenCrossRefGoogle Scholar
  9. 9.
    Montgomery DC (2013) Design and analysis of experiments, 8th edn. Wiley, HobokenGoogle Scholar
  10. 10.
    Mukerjee R, Wu CFJ (2006) A modern theory of factorial designs, 1st edn. Springer, BerlinzbMATHGoogle Scholar
  11. 11.
    Mukerjee R, Wu CFJ, Chang MC (2017) Two-level minimum aberration designs under a conditional model with a pair of conditional and conditioning factors. Stat Sin 27(3):997–1016MathSciNetzbMATHGoogle Scholar
  12. 12.
    Sabbaghi A (2019) An algebra for the conditional main effect parameterization. Stat Sin.  https://doi.org/10.5705/ss.202018.0041 CrossRefGoogle Scholar
  13. 13.
    Su H, Wu CFJ (2017) CME analysis: a new method for unraveling aliased effects in two-level fractional factorial experiments. J Qual Technol 49(1):1–10CrossRefGoogle Scholar
  14. 14.
    Sun DX (1993) Estimation capacity and related topics in experimental designs. Ph.D. thesis, University of WaterlooGoogle Scholar
  15. 15.
    Wang JC, Wu CFJ (1991) An approach to the construction of asymmetrical orthogonal arrays. J Am Stat Assoc 86:450–456MathSciNetCrossRefGoogle Scholar
  16. 16.
    Woodward JA, Bonett DG (1991) Simple main effects in factorial designs. J Appl Stat 18(2):255–264CrossRefGoogle Scholar
  17. 17.
    Wu CFJ (2015) Post-Fisherian experimentation: from physical to virtual. J Am Stat Assoc 110(510):612–620MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wu CFJ (2018) A fresh look at effect aliasing and interactions: some new wine in old bottles. Ann Inst Stat Math 70(2):249–268MathSciNetCrossRefGoogle Scholar
  19. 19.
    Wu CFJ, Hamada MS (2009) Experiments: planning, analysis, and optimization. Wiley series in probability and statistics, 2nd edn. Wiley, HobokenGoogle Scholar
  20. 20.
    Ye KQ (2003) Indicator function and its application in two-level factorial designs. Ann Stat 31(3):984–994MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA

Personalised recommendations