Waterfall and Six Sigma

At the highest level, the most commonly used software development lifecycle methodology, called the Waterfall Model, can be summarized as the following sequential series of steps:
1 Requirements and Specification
2. Design
3. Construction (Coding)
4. Integration
5. Testing
6. Deployment
7. Maintenance
From this high-level view, the Waterfall Model looks like an ideal process where the output of one step is the input into the next, finally resulting in the deployed software. Because of this process view, it would seem that Six Sigma, more specifically DMAIC, could help solve the issues outlined above and help improve the Waterfall process to deliver higher quality software on time.