Since we are picking nits, here's my personal peeve with the PDCA model:
"Plan" seems like something that should be part of "Do" (or "Act"). Good processes have documented instructions, objectives, and expectations. These should be set in the last "Act", and available at points of use with the QMS. Why do we need a separate "Plan" step?
Furthermore, I think "check" muddles together observation (measuring) with diagnostics (compare, investigate). Those two tasks should be separate things.
So here is a different model: "PAD-UP" Produce, Assess, Diagnose, UPgrade.
- Produce: Execute or perform the process
- Assess: Observe. Measure process outputs and receive feedback from observers (process clients, participants and other parties)
- Diagnose: Compare with expected results, Investigate root causes.
- UPgrade: Improve process. Upgrade standards, instructions, objectives and expectations. Document in QMS.
And here is the new graphical representation that you're looking for, the "Stairway to Quality":
