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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.
Leaving the tank at factory pressure and setting the pressure control switch to a higher cut-in/cut-out pressure means that the volume of water you can draw from the tank before the pump turns on is a bit reduced. Details about how to adjust the water pressure control switch are at PRESSURE CONTROL SWITCH ADJUSTMENT. had to put a new pressure switch on, the pump was running all the time and it burn the points up. The new one is letting the pump run all the time too, when the pump is running the water pressure keeps going up and down, until there is a small amount of water coming out.