Oftentimes, we talk of processes & improving them in the project management space. In fact, a seamlessly integration of teams & its various processes is the state that every project manager wishes to take her team to & make it stay there. As frequently stated in many PM books, teams go through typical stages of the formative, the storming or conflicting, normative or the settlement & appearance of coherence, & finally performing.
I'm not sure how to measure the maturity of a process, or indeed if there are metrics that can be captured or surveys that can be conducted to capture this kind of information - which, for all you know, might just be little more than opinions - but there is a part of me which tends to relate process maturity to a ritual.
Now, firstly by ritual I do not mean blind compliance. By ritual, I mean a stage of process evolution which has more or less perfected the process, i.e. it has answered all doubts & concerns. The term ritual is useful then in describing what follows, for in that stage of maturity there is a comprehensive buy-in of the process by all parties concerned & there is a degree of automation in the way the process is followed - without reminders or any assertions.
Like a ritual then, process compliance becomes a part of a larger, collective conscience.