I think the Six Sigma process can be integrated with the Project Planning Process (PPP) very easily. Both are related to the Plan. Do. Check. Act cycle.

The PPP is comprised of initiating, planning, executing, closing, and monitoring and controlling. Six Sigma changes based on methodology and can either be define, measure, analyze, improve, and control (DMAIC) or define, measure, analyze, design and verify (DMADV). The “Plan” stage of PPP and Six Sigma is initiating and planning, and define and measure. The “Do” stage of PPP and Six Sigma is executing and closing and analyze, improve, and design. The “Check” and “Act” would be monitoring and controlling, and control and verify.

https://books.google.com/books?id=H63NBQAAQBAJ&pg=PA466&lpg=PA466&dq=six+sigma+official+PDCA&source=bl&ots=TCMF7dg08b&sig=bVIMT61Ig1wgTKe53SFHkzmWfSk&hl=en&sa=X&ved=0ahUKEwj0mYvz-JnSAhXpy4MKHQfbAC8Q6AEIPzAI#v=onepage&q=six%20sigma%20official%20PDCA&f=false

Jones, Erick C. “Quality Management for Organizations Using Lean Six Sigma Techniques.” Google Books. CRC Press, Taylor and Francis Group, n.d. Web. 18 Feb. 2017.