I was finally able to test fire my new build last night. I was using XM855 ammo out of two brand new Magpul generation 3 PMAGs. Lower has an Anderson Arms lower parts kit with JP reduced power springs. The hammer appears to have been lightened from milspec, it doesn't have the curved hook on the back end of it.

First magazine fired perfectly, no issues. Bolt locked to the rear when magazine was empty.

On second magazine I started having failure to fires. These literally started occurring every second shot. I would pull the charging handle, eject the round that didn't fire, chamber another round and fire, attempt to fire a second round, it wouldn't fire.

Upon inspection of the ejected rounds it appears their primers are dented, but they didn't fire. Light primer strikes.

I've done some searching online, and it appears that the primary cause of this is the hammer spring not being installed correctly. I will quadruple check this tonight after work. I am fairly certain I installed them correctly, I used to do this for the military and I followed an online tutorial while doing it.

Assuming the springs are installed correctly, is my problem likely to be from the lightened hammer and JP reduced power springs just not having enough force to work consistently with XM855 primers? I consulted with a friend of mine who shoots competitively and he suggested just replacing the hammer spring with a milspec hammer spring. I have one on hand so I will try it out, but are there any other areas I need to look at?

Thank you.

Also, if it matters, the rounds where ejecting at approximately the 4 o clock position from the rifle. I do not think the weapon is over gassed. I recorded the test fire and confirmed this from watching the video.

Put a mil spec hammer spring back in.

This is an easy fix. ;)

place the stock springs (mil-spec) springs in at most your talking about .5 pounds loss on the trigger pull. JP also sells some "tactical" springs.

I've had the same problem with PMC ammo, but it had take 3 cases for the problem to appear.

Trash the JP Yellow springs.

Replacing the JP spring with the milspec did not fix the issue. I've ordered a ALG trigger and hammer to see if this fixes the problem. They should arrive today. Someone elsewhere was able to point out three people who had similar issues with Anderson Arms hammers and/or disconnectors, stating the problem is with burs on the hammer and/or disconnector.

I doubt an ALG trigger will fix your problem.  If a standard hammer spring isn't lighting the primer after your hammer drops, the carrier probably isn't closed 100%.

While jaqufrost may be on to something, you may want to look at this thread as it maybe a sear issue with your Anderson hammer.
Troubleshooting

If he's got a dead trigger after the first shot it is likely a sear problem. If he can pull the trigger and hear the hammer fall but the primer doesn't ignite it's more likely to be a carrier that hasn't fully closed.