Interaction Plot

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Interaction


Purpose

An interaction exists between Factors when the effect of one Factor upon the Response variable changes depending on the level of the other Factor(s). Interactions can be seen in an Interaction Plot.

DOE can help you quickly and efficiently discover the optimum conditions that produce the best quality. Trial-and-error is the slowest method of discovering these optimal conditions and usually misses the effects of various interactions.

DOE significantly reduces the time and trials necessary to discover the best combination of factors to produce the desired level of quality and robustness.



Anatomy

Interaction Plot

Reference: Understanding Industrial Experimentation

Terminology

A. First experimental Factor.

B. Response variable.

C. Response when first Factor is at lowest setting and second Factor is at highest setting.

D. Response when first Factor is at highest setting and second Factor is at highest setting.

E. Response when first Factor is at lowest setting and second Factor is at lowest setting.

F. Response when first Factor is at highest setting and second Factor is at lowest setting.

When no interaction exists between Factors, there is no difference in the Response between the levels of one Factor, when the other factor changes.

Significant interaction means that as one Factor changes state from low to high level, the Response changes significantly depending on whether the other Factor is at a high or low setting. Significant interaction can mask the significance of main effects.

Interaction Plot


Purpose

To graphically represent the impact that a change in a process input has on the experimental response.

Anatomy

Interaction Plot

Reference: The Vision of Six Sigma

Terminology

A. Vertical Scale is the units of the Response variable.

B. Horizontal Axis is the second of the two Factors.

C. Horizontal Axis scale presents the different levels of the second Factor.

D. Line representing the change in the response variable when the second Factor goes from one level to another, when the first Factor is at its lowest level.

E. Line representing the change in the response variable when the second Factor goes from one level to another, when the first Factor is at its highest level.

F. Legend displaying the attributes of the symbols and lines for the levels of the first Factor column.


Major Considerations

An Interaction Plot is typically a second step in the ANOVA process. A Main Effects Plot is first used to demonstrate the Main Effects of a Factor, then an Interaction Plot is used to visualize the presence of interactions of the Factors.

Evaluating interactions is very important because they can cancel out or magnify factor main effects.

Application Cookbook

1. Collect data and present in the form of a matrix.

  • The first column contains the levels of the first Factor.
  • The second column contains the levels of the second Factor.
  • The third and subsequent columns contain the Response values measured at the settings of the first and second Factors.
  • If multiple raw Responses are presented in separate columns, the Mean Response should be calculated.

2. Prepare a graph showing the Response scale as the vertical axis, and the setting levels of the second Factor as the horizontal axis.

3. Plot the Mean Responses for the second Factor at its various levels, with the first Factor at its lowest setting. If the second Factor only has two levels (i.e. low and high), the graph will be a simple straight line connecting the two points. If the second Factor has multiple levels, the plot will consist of a series of points joined with straight lines.

4. Repeat the previous step, with the first Factor at its next lowest setting.

5. Continue the process until all levels of the first Factor have been addressed.

6. Interpret the chart:

  • The more parallel the lines at the different Factor settings, the less the interaction.
  • Perfectly parallel lines show no interaction.
  • Slightly non-parallel lines imply a slight interaction between the Factors.
  • Lines which cross indicate clear evidence of an interaction between the Factors.

From Interaction Plot to Six Sigma Tools.

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