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Sub MOA AR 15

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Sure. WOA or Craddock Precision barrel and a Geissele trigger and you're halfway there. Hell, for under $700 you can buy a complete Rock River Arms NM upper. With the right ammo mine is absolutely capable of 5 shot sub MOA groups. A very underrated upper.
 
Is it possible to assemble a sub MOA AR15 with a 16" barrel? if it is what components are critical for such a build?
Yes, its easy... to get AR 10 & AR 15 to run under 1 MOA.
Every AR I build will shoot a few loads under 1 MOA, some a 1/4" to 1/2" for 5 shots..

"Build" requires more than just "assemble"...
A good (expensive) barrel is usually a good place to start, although a cheap barrel will get it done, sometimes...
Really cheap fmj military ammo won't cut it. Even factory ammo is not up to snuff, most of the time.
I shoot handloads in everything.
The last photo is two 6 mm ARCs in AR 15 same match ammo ...top is a factory "assembled" upper 5 shots 2.5".
Bottom is a AR 15 "build"...with the Proof Research barrel, 5 shots 1/2" on the first try...big difference.
 

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Is it possible to assemble a sub MOA AR15 with a 16" barrel? if it is what components are critical for such a build?
100% able to make sub-MOA AR's. Barrel to receiver fit is very important. I prefer a thermal-fit upper like Bravo Company and a good barrel free floated, and a good trigger. That's 70% of the needed combo. The Last 30% is shooter and ammo. Lots of good factory ammo out there.

Good luck.
 
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I think he means regression analysis.
I mean applying the basic scientific method to building the rifle in question. Does your ammunition favor your rifle? I dunno, does it? Let’s find out. What barrel nut torque provides favorable harmonics? I dunno, let’s find out.

By manipulating the variables likely to contribute to precision, you will turn a good rifle into a great rifle, and a great rifle to a super rifle. Starting with quality parts is a prerequisite, but fine tuning via experimentation and the application of accepted best practices will only improve on that.

Or you can just crank parts together and hope for the best. Sometimes it works out, sometimes it doesn’t.
 
It's different from the scientific method. Same same, but different.
Thank you for letting me know that you knew that. Not only were you so smart to know that, but you were smart enough to know what I meant anyway.

Anyway, sub-MOA is very doable from a semi. Tweaking variables helps. Having good components to tweak helps more. What I find helps is eliminating any jump from the receiver feedramp cuts to the barrel extension ramp portion. A lot of times they’ll have sharp jumps between, or sharp teeth on the side that, if smoothed out, won’t gouge into the bullet and I find my groups will noticeably tighten up after I’m done.
 
OP - Should be pretty clear from some of the answers you're getting that assembling a sub MOA rifle is doable. However, whether YOU are capable of assembling a rifle and then getting sub MOA results is a different question.

Not trying to be insulting here, but simply putting together a list of components only takes you so far. What experience do you have assembling uppers? Are you mechanically inclined and willing to tweak your rifle to get the best performance? Do you reload and are you willing to spend time experimenting with different bullets, powders, seating depths, etc.? And finally, and perhaps most importantly, how good a shooter are you?

At the end of the day, you can't buy skill - although many have certainly tried. Ending up with a rifle that consistently shoots dime sized groups requires a bunch of things to come together. The right components, the right builder, the right ammo, and the right shooter. And a little luck probably doesn't hurt either.