How To Know If a Fuse Will Work Properly?
I think maybe you misunderstand how a fuse behaves.

A fuse doesn't instantly open when current meets the Ampere Rating. There is a minimum Opening Time at 100% of Ampere Rating, and there will also be maximum Opening Time at higher currents such as 200% or 1000% of Ampere Rating.

For example, a Littelfuse 0251005.NRT1L (data sheet http://www.littelfuse.com/~/media/electronics/datasheets/fuses/littelfuse_fuse_251_253_datasheet.pdf.pdf ) lists the following:


100% of Ampere Rating: Opening Time 4 Hours Min
275% of Ampere Rating: Opening Time 300 ms Max
400% of Ampere Rating: Opening Time 30 ms Max
1000% of Ampere Rating: Opening Time 4 ms Max


So this 5A fuse with 5A of current flowing through it, is guaranteed NOT to open for at least 4 hours. But when the current exceeds 13.75A, this fuse is guaranteed to open within 300 ms. If the current reaches 50A then the fuse opens very quickly. But if the current is only 10A, the fuse won't open instantly.

If you use a 2A Ampere Rating fuse instead, then the 275% of Ampere Rating poing is 5.5A, which is closer to what you want in your example. But if your application typically draws more than 2 amps, then the 2A rated fuse will blow sometimes. Especially if the equipment is left on for a long period of time.

Fuses just don't have a very tightly controlled "open fail" current. They are one-time-use devices; once a fuse is tested to the point of opening, that fuse is permanently destroyed -- so statistical process control is the only practical way to ensure that the fuses are likely to work.

You could perform the same kind of testing. If you're building a batch of 500 devices, purchase a reel of 5000 fuses. (Again I'm assuming picofuse, which look similar to axial leaded 1/4 watt resistors. Glass tube fuses don't come in tape and reel.) When you get that big batch of fuses, you randomly pull out some samples, maybe 100 fuses. Test at two different conditions: 
 - must sustain current below 100% Ampere Rating for xx time
 - must always open within xx time at test current 275% Ampere Rating (this is the destructive part of the test)

The more fuses you test, the more closely the tested sample will resemble the untested fuses, and the more confident you will be that the fuses work as advertised. But the more time and money you will be spending, to fill the trash can with used fuses.

Further downside is that if you conclude from your testing that this particular reel of fuses is not up to your standards, the distributor might not accept returns of a partial reel. So you'd be out $1400.