Appendix: Definition

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  • Factor (X) : a variable that is controlled in the experiment.
  • Level : the value assigned to a factor in an experiment.
  • Essay: a line on the plan, meaning a combination of levels to be built.
  • Interaction : The effect of one factor depends on the level of another. This cannot be inferred from any factor-by-factor analysis.
  • Alias : two effects that are confounded by the design of the study—there is nothing in the data to distinguish between them.
  • Resolution : Severity of aliases. III = main effects confounded with interactions; IV = unconfounded main effects; V and higher = negligible confounding.
  • Orthogonality : There is no correlation between two columns in the design; their effects are estimated independently.
  • Central Point : Test in the middle of the range for all factors. Measures repeatability and reveals curvature.
  • Replication : Revise the plan to remove the aliases, even if it means doubling the number of tests.
  • Degrees of freedom (DOF) : Number of coefficients to be estimated. Lower bound on the number of trials.
  • Complete Map : all combinations of levels. No aliases, maximum cost.
  • Fractional Plan : a selected portion of the complete plan. Fewer trials, or in other words, as a trade-off.
  • DSD (Definitive Screening Design) : a 3-level screening plan that partially detects curvature without confusing the main effects with the interactions.
  • Response surface methodology (RSM) : a complete quadratic model—linear, interactions, squares—used to locate an optimum.
  • Cube-to-Sphere Ratio (α) : distance between the star points of a composite plane, in coded units.
  • Filling plan : a plan aimed at achieving uniform coverage of the space, without assuming any specific model.
  • Audze-Eglais : criterion for filling the space; the lower the value, the better.
  • MaxPro : criterion for filling in projections; useful when only a few factors are actually active.
  • D-optimality : a criterion for selecting a subset of tests that maximizes the determinant of the information matrix for a given model.
  • Certified Plan (Smart DOE) : a design for which the orthogonality of the main effects and the absence of aliasing with the second order are mathematically proven and rechecked with each delivery.