Pressure Switch

I will illustrate this with a common example: a pressure switch that starts a fan on rise of refrigerant condensing pressure, and then shuts the fan back off when the pressure falls. For example, as the pressure rises above 9 bar, the fan starts; then, when the pressure drops below 7 bar, the fan stops.

In your terms, the "on measurement increase" value is 9 bar, the "on measurement decrease" value is 7 bar, and the "deadband" is the difference, namely 2 bar.

For close control of the measured variable, a small deadband is desirable; to avoid too-frequent starting/stopping of motors, a larger deadband is desirable. This is a matter of compromise and experience according to the application.

"Deadband pressure range" would apply if the deadband is adjustable. In the given example, the deadband was 2 bar, but it might be from a fraction to a few bar. (Or whatever units you may be using.)

Some other terms you might see are "cut-in point" and "cut-out point."

http://hvacrfundamentals.blogspot.com/2016/04/pressure-switch-lingo.html