As a process of systematic study and analysis, TRIZ makes problem solving easier. One characteristic of the TRIZ approach is its ability to break down problems into more manageable and understandable pieces. This is actually what you need to do when you are faced with a challenge.
The discipline of TRIZ allows you to do this. Thus, if you are to fit it into your Six Sigma methodology, you find at which stage in the DMAIC cycle it will be. Will it be in the Define stage, or in the Control stage?
Ferret.com in one of its problem-solving articles suggests:
The use of TRIZ is a standard recommendation for the Improve stage in the DMAIC cycle and forms an essential part of the Design for Six Sigma process…
Continuous improvement – The constant switching in TRIZ reasoning between the large picture view and minute detail ensures that improvements are carried out efficiently. The quest for increasing ideality provides the motivation for sustaining such programs within the organisation.
Link: Problem solving: looking back to go forward