DOE Inner Array

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Purpose

An Inner Array is used to systematically account for the effects of experimental Factors that are beyond the control of the experimenter, by introducing a second, ancillary, experimental design consisting solely of uncontrollable environmental Factors.

The Inner Array forms half of an experimental design known as the Taguchi approach, and is used in conjunction with an Outer Array.


Anatomy

Inner Array

Reference: Understanding Industrial Experimentation

Terminology

A. The Inner Array, also known as the Design Matrix.

B. The Outer Array, also known as the Noise Matrix.

C. An experimental Factor (B).

D. An experimental run.

E. One Response acquired per run for each of the environmental Factors.


Major Considerations

The Inner Array is also known as the Design Matrix. For each run of the Inner Array, one Response is collected for each setting of the environmental factors.

Therefore, each "set" of Responses for each Design run corresponds to one sub-group of size n, where n is the number of runs of the Noise Matrix. Minitab limits Taguchi designs to two-level designs.

Application Cookbook

1. Select the experimental design, based upon the number of Factors, levels, desired precision, etc.

2. Select the environmental (noise) factors over which there is little or no control.

3. Select a 2k experimental design where k is the number of noise factors.

4. Determine the high and low factor settings for the k noise factors.

5. For each of the runs in the main experimental design (the inner array), collect one response point for each combination of noise factors.

6. Continue the experimental runs until 2k*n, Responses have been collected. "n" is the number of runs in the inner array.

7. Each of the k Responses for each run corresponds to one sub-group.

From Inner Array to Six Sigma Tools.

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