Terms and Definitions

Response

The response is the result of the experimental measurements.

Factor

The factors are the variables of the system that, when changed, may have an effect on the response.

Levels

The levels are the values each factor are set to in the design.

Run

A run is a single measurement or in the design.

Interaction

If a level change of a combination of factors has an effect on the response, and those factors have no effect when changed individually, those factors are said to have an interaction.

Confounding

If effect of either a factor or an interaction of factors cannot be measured independently of all other factors and interactions, the effects that cannot be measured independently are confounded.

Orthogonal

Vectors of the same length are orthogonal if the sum of their products is 0.

An experimental design is orthogonal if the effects of any factor sum to zero across the effects of the other factors.

Balanced

An experimental design is balanced if all combinations of factor levels have the same number of runs.

Design Word

A confounding relationship that characterizes a design.

Design Generator

A design word, i.e. a confounding relationship, used to generate an experimental design

Defining Relationship

The total collection of design words that are held constant to define the fraction in a fractional factorial design. A $2^{k-p}$ design has $2^p$ design words.

Resolution

The extent of confounding present in a design.

Resolution III

Main effects are confounded with two-factor interactions.

Resolution IV

No main effects are aliased with two-factor interactions, but two-factor interactions are aliased with each other.

Resolution V

No main effect or two-factor interaction is confounded with any other main effect or two-factor interaction, but two-factor interactions are aliased with three-factor interactions.

Resolution $\infty$

No confounded is present in the design.