"Monitoring the software engineering process" is quite literally management's job. If they can't be bothered to do it and I'm supposed to do it for them, I'd like a raise. A big fat one. And the title and expense account to go with it.

Oh, that's not in the cards? Do your job, then. Figure it out. If you can't perhaps you're not fit to manage engineers.

Software engineering is an empirical process, not a deterministic one. Can't handle that? Get out.