testing heater A/C blower resistor

So much brand variety in my history that I cant say definitely but... I'm pretty sure these resistors accumulate. Each switch positon, wire, fan speed change, routes current through just 1, or 2, or all 3 resistors, except HI which is direct battery voltage, no resistor.
The most typical fault condition I've seen is only HI fan speed works. The one resistor that broke interrupted all 3 paths. I can't say why they fail in that manner.