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Results for Two-Level Designs with General Minimum Lower-Order Confounding.

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This study details the general minimum lower-order confounding (GMC) criterion for two-level designs. It focuses on calculating key elements of the aliased effect-number pattern (AENP) for optimal experimental design selection.

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Area of Science:

  • Statistics
  • Experimental Design

Background:

  • The general minimum lower-order confounding (GMC) criterion, proposed by Zhang et al. (2008), is crucial for selecting optimal two-level experimental designs.
  • The criterion relies on the aliased effect-number pattern (AENP) to understand confounding information.

Purpose of the Study:

  • To investigate the properties of the aliased effect-number pattern (AENP) in two-level general minimum lower-order confounding (GMC) designs.
  • To elucidate the internal principles for calculating the leading elements (1 (#) C 2 and 2 (#) C 2) within the AENP.

Main Methods:

  • Analysis of the aliased effect-number pattern (AENP) ordering to prioritize lower-order factor effects.
  • Derivation of mathematical formulations for specific GMC 2 (n-m) designs based on two distinct cases of 'n' relative to 'N'.

Main Results:

  • The study provides a detailed understanding of the confounding information inherent in two-level GMC designs.
  • Mathematical formulas for calculating the leading elements of the AENP are established for specific design ranges.

Conclusions:

  • Understanding AENP properties is vital for effective application of the GMC criterion in experimental design.
  • The derived mathematical formulations offer practical tools for selecting optimal two-level GMC designs.