I cannot get what's a problem.
It looks work correct.

What is it that works correct?
Our environment is given up the top of this JIRA,

Expected behaviour is that Jenkins uses some heuristic to detect that a build is "likely stuck.
But when we use this option it just aborts immediately, as shown.

A build can't possibly be stuck after 0 minutes.
We occasionally get builds that are genuinely stuck, we notice this after maybe 3 hours or more.
It would be useful if this feature worked so we could use it to abort those.
If the feature aborts every build after 0 minutes it's not much use though.

In fact from the timestamps it looks like the build was aborted after 4 seconds. Surely the 'isLikelyStuck' heuristic should never conclude that a build is likely to be stuck after such a short time?

"0 minutes" means a time less than 1 minutes.
And it is a correct behavior if the job always finish in 1 seconds.

What's your problem ?
Build-timeout triggers timeout too sooner than the job always finishes?
Or build-timeout should not trigger timeout so soon if the job always finish too soon ? (for example, adding a field for shortest timeout?)

I want to know followings:

• Does it happen to any jobs? Or It happens to a specific job?
• If it happens to a specific job, steps to reproduce the problem.
• Time the job always finishes.

Problem is that "build timeout" triggers against a build which is progressing normally, not stuck. It triggers almost immediately, which seems pointless.

I cannot reproduce. What I tested:

Environment: With Jenkins-1.509.2, Build-timeout 1.14 on Windows 8 64 bit, Java 1.7.0_45
Steps:

1. Create a free style project.
   • Enable "Abort the build if it's stuck"
     • Time-out strategy: Likely stuck
     • Time-out variable: TIMEOUTVALUE
       • This is added in Build-timeout 1.13. You can get the build timeout milliseconds
   • Add "Execute shell" ()

     echo ${TIMEOUTVALUE}
     sleep 180
     

2. Run a build. The log was:

   Started by user anonymous
   Building in workspace C:\Users\ikedam\.jenkins\jobs\timeouttest\workspace
   [workspace] $ sh -xe C:\Users\ikedam\AppData\Local\Temp\hudson7811755437042469206.sh
   + echo 86400000
   86400000
   + sleep 180
   Finished: SUCCESS
   

3. Run a build again. The log was:

   Started by user anonymous
   Building in workspace C:\Users\ikedam\.jenkins\jobs\timeouttest\workspace
   [workspace] $ sh -xe C:\Users\ikedam\AppData\Local\Temp\hudson670841287852715641.sh
   + echo 1803440
   1803440
   + sleep 180
   Finished: SUCCESS
   

As far as I tested, It worked perfect.
And as far as I reviewed the code, it should work as Executor#isLikelyStuck() does as described in the help text.