I actually prefer a systems lifetime as the 4th dimension.
Quality is just a function of the system time to live being fit against the other three constraints. Scope, budget and time. (I'd actually say time is a subset of budget.)
To be honest, most "deadlines" are really just cost boundaries in the first place.
If you're not publicly traded and made an announcement about something going live on a certain date, or have a regulatory body that requires something by a certain date, your deadline is just a cost-cutting measure.