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Deadband is also known as hysteresis and is the amount of a measured variable (pressure, temperature, etc.) between the point where a switch closes and then re-opens. It can be implemented is software if you have an analog input (i.e., open at 1.02 PSI, close at 0.98 PSI) or designed into a switching mechanism. Often the deadband of a switch is fixed and cannot be adjusted. A typical example is in a wall thermostat in your house.
If it is not showing a pressure of 30-50 psi or 40-60 psi (slightly left of center) that could be your problem. The electrical switch at the pressure tank (grey box) is a fairly common cause of failure in the pump/private well water system; so check the switch to make sure it is working. Manually closing the pressure control switch should turn the pump on.