How to detect MOSFET's open or not
Note: I have noticed that some people use the term "open" for conducting, which is in direct conflict with "open" as in "open circuit" (not conducting) as we use in North America, at least. It would be better to use some other term. 

Threshold voltage is specified at a given Id. So if you apply a constant current (with limited voltage) or simply connect a properly selected resistor from drain to supply rail and then apply Vgs(th) you should see a Vds that results in a higher current than the specified for Vgs(th). 

For example, if Vgs(th) is specified as 2V with Id = 250uA you could use a 20K resistor to 10V. Then apply 2V and Vds should be less than 5V. I picked the resistor for a 5V drop (half the presumed supply) at 250uA current. 

When Vgs = 0 (assuming enhancement mode transistor) the Vds should be close to the supply voltage. 

The gate current in both cases should be within specifications (probably too low to easily measure). 

Example schematic for a Device Under Test that is an N-channel enhancement-mode MOSFET. 







simulate this circuit &ndash; Schematic created using CircuitLab

That will detect most gross faults with a MOSFET.