How is a BOP tested?

Im sure rigs have turn arounds. During that time it is probably activated/tested by actually operating/triggering it. Testing it with a rig in place would be easy to do as it would be easy to confirm that it works.

Just a guess though!

The subsea BOP typically consists of the following (top to bottom)
-An annular preventer which consists of a round rubber element. the element is driven into the bore of the bop stack and seals around the drill pipe that is in the hole. some BOP stacks have 2 annulars, some only have 1. they are tested on a 14 day cycle and function tested weekly
-a set of blind shear rams. these are hydraulically actuated rams that are driven into the bore of the stack cut the pipe that is across the stack then hold pressure after cutting. they are pressure tested from below every 30 days
-several sets of pipe rams. these are hydraulically actuated, steel rams that are driven into the main bore of the bop, and close and seal against the DP that is across the stack. sometimes they are designed to close against a specific size of drill pipe (like 6 5/8") sometimes they are designed to close against multiple sizes (variable bore rams from 3 1/2 - 7 5/8" - for example). these are tested from below every 14 days and function tested every 7 days.

For a function test, you simply execute the desired functions from surface and monitor the control panel for confirmation that it took place.

For a pressure test, a test plug is run in the hole and landed in the wellhead. the desired ram or annular is closed and pressure is applied down 1 of 2 high pressure, steel lines (the choke or kill line) that go from the rig floor to the BOP and are designed to hold 10-15,000 psi. the pressure is applied to the top of the test plug (so it never is applied down the hole beyond that) and is applied to the bottom of the rams.

A key point is that BOP rams are desinged to hold pressure from the bottom. you can eliminate the test plug by taking a regular set of pipe rams and installing them upside down so they hold pressure from above as well. this is nice to do if the stack configuration allows it because it saves time.

The test pressure is based upon the maximum anticipated wellhead pressure that is calculated prior to drilling the well. this pressure is approved by the MMS in the permit to drill.

All of these tests are charted, dated, and signed by key personnel on board. the MMS inspector, when he lands on board, will review these test charts in extreme detail and write an incident of non-compliance if there is any irregularity.

also note that while shear rams are designed to cut and seal, they will not cut everything on earth. rigorous shear testing is typically conducted at the BOP vendor's facility if there is a question as to something's "shearability".