## Six Sigma X-Y Matrix Explained

written by: Suvo • edited by: Marlene Gundlach • updated: 7/13/2009

X-Y matrix, a project management tool, is also called cause and effect (C&E) matrix. This article will explain six sigma X-Y matrix project management tool and includes an example.

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X-Y matrix project management tool (or cause and effect matrix) is used mainly in six sigma DMAIC project. This is the ideal tool for prioritizing the input process parameters (X’s). The prioritization of X’s is important for performing process FMEA.

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### Procedure for Making an X-Y Matrix

• List out the CTQ (Y’s) for the targeted process.
• Make a table with numbers of rows and columns.
• Write down the CTQ against individual column.
• Write the weightage for each CTQ.
• Find out input process parameters (X’s) by brainstorming and write them against individual rows.
• Put suitable numbers in the intersection of rows and columns to show the relationship between X’s and Y’s.
• Finally calculate the weighted sum against each X’s.

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### An Example

Let’s take the example of the newspaper printing process. After transforming the VOC we find the CTQ (Y’s) as below:

• Good quality photo
• Harmless to health

Upon brainstorming, the input process parameters (X’s) have been found as below:

• Good quality ink
• Less vibration during operation of printing press
• Paper quality

For the above sets of X’s and Y’s the X-Y matrix table will look like the example below:

Wherever there is a strong relation between X’s and Y’s, put 9. For weak relations put 3 or 1. Keep the intersection field blank if there is significant relation.

Weighted sum for “Good quality ink" is calculated as 15*9 + 10*9 + 10*1 = 235. The calculation is similar for the rest of the X’s. The input parameters with a higher weighted sum should be selected for further FMEA.

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### Conclusion

A X-Y matrix project management tool is useful for prioritizing the input parameters (X’s). CTQ (Y’s) of the six sigma project must be kept ready before preparing the cause and effect matrix. The X-Y matrix should be prepared by brainstorming of cross functional team members.The success of FMEA also depends upon the result of X-Y matrix.