The *matrix diagram* is used to show relationships between a single set of factors or between 2 or more sets of factors. It differs from the *prioritization matrix* in that the prioritization matrix tries to quantify the ranking among the factors. The matrix diagram gives a qualified relationship between the factors, denoting the relationship with symbols like + for a positive relationship or a – for a negative relationships.

An example of this can be found in the House of Quality tool that demonstrates the method of Quality Function Deployment (this image is taken from Wikipedia).

Notice the “roof” of the house which contains the relationships between the various design features proposed for this product development. If two factors influence each other positively, there is a circle, with a dot in the circle for a strong positive influence. On the other hand, if there is an X, that means there is a negative influence between the factors. If the influence between the factor is weak, there is a triangle. This is, of course, a single example; other companies may use other symbols to represent similar types of relationships.

By the way, you may notice that in the “basement” of the House of Quality model, there is a list of weighting factors underneath each design feature which demonstrates an example of the *prioritization matrix* that was talked about in the last post.

In fact, you can convert a matrix diagram into a prioritization by taking each of the symbols for strong, medium, or weak relationships (both positive and negative) and assigning them a weighting factor from 0 to 9 and then adding up the various values for the symbols.

Finally, the website http://www.syque.com/quality_tools/toolbook/Matrix/how.htm gives the following examples of the different types of matrices that can be used to compare a set of factors (L-type matrix), two sets of factors (T or X-type matrix), or even three sets of factors (C-type or Y-type) in a three-dimensional matrix.

The matrix diagram is therefore used to chart the complex interrelationships between various one, two, or three sets of factors. It is used to focus on the complicated details of a particular aspect of a problem that has been previously identified and broken down using some of the other tools mentioned in previous posts in this series.

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