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Lean Six Sigma Black Belt

# Experimental Methods

The Experimental Methods for Design Experiments are as follows:

First-Order: Refers to the power to which a factor appears in a model.

Fractional: An adjective that means fewer experiments than the full design calls for.

Full factorial: Describes experimental designs which contain all combinations of all levels of all factors. No possible treatment combinations are omitted.

Input factor: An independent variable which may affect a (dependent) response variable and is included at different levels in the experiment.

Inner array: In Taguchi-style fractional factorial experiments, these are the factors that can be controlled in a process.

Interaction: An interaction occurs when the effect of one input factor on s the output depends upon the level of another input factor.

Level: A given factor or a speciﬁc setting of an input factor four levels of a heat treatment may be 100°F, 120°F, 140 F, and 160°F.

Main effect: An estimate of the effect of a factor independent of any other factors.

Mixture experiments: Experiments in which the variables are expressed as proportions of the whole and sum to 1.0

Multi-Collinearity: This occurs when two or more input factors are expected to independently affect the value of an output factor, but are found to be highly correlated.

For example:

An experiment is being conducted to determine the market value of a house. The input factors are square feet of living space and number of bedrooms. In this case, the two input factors are highly correlated. Larger residences have more bedrooms.

Nested experiments: An experimental design in which all trials are not fully randomized. There is generally a logical reason for taking this action.

For example, in an experiment, technicians might be nested within labs. As long as each technician stays with the same lab, the techs are nested. It is not often that techs travel to different labs just to make the design balanced.

Optimization: Involves finding the treatment combinations that give the most desired response. Optimization can be “maximization” (as, for example, in the case of product yield) or “minimization” (in the case of impurities).

Orthogonal: A design is orthogonal if-the main and interaction effects in a given design can be estimated without confounding the other main effects or interactions. A full factorial is said to be balanced, or orthogonal, because there are an equal number of data points under each level of each factor.

Outer array: In a Taguchi-style fractional factorial experiment, these are the factors that cannot be controlled in a process.

Paired comparison: The basis of a technique for treating data so as to ignore sample-to-sample variability and focus more clearly on variability caused by a specific factor effect. Only the differences in response for each sample are tested because sample-to-sample differences are irrelevant.