At the first sight, it may sound this is ridiculous. Why? Because they have different goals. Yes, Six Sigma has as one of its goal to reduce the process variation while Agile is for not using defined process control.
Despite this, there are a few sections where they are doing a great job together. For example, Requirements Management. It is a very good idea to apply Six Sigma in Requirements Gathering in Agile and I strongly recommend this. Please keep in mind that Requirements errors are very expensive to fix at a later point, even in Agile, which is by definition adaptable during the Sprints.
The Voice of the Customer techniques can be used to emphasize this Requirements Gathering, being very well known and documented in Six Sigma.
Also, building a Critical to Quality Tree helps the teams to brainstorm a solution from a requirement, which is often quite vague.
Failure Mode and Effects Analysis for Design can also be successfully applied in Agile and by doing this we could avoid the extra-costs of the Sprints, so of the whole project.
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