What is RTCP XR?
RTCP XR is a relatively new mechanism for compatible devices to transmit voice quality reports after the conclusion of a call. Asterisk internally has some metrics (RTPAUDIOQOS, for example) to monitor call quality, but the piece Asterisk sees is only half the picture. RTCP XR lets us measure what the end user's experience is.
Newer firmware for the Cisco SPA50x and SPA525 series phones has this capability. I am told some Polycom devices do as well, as do SNOM phones.
How does it work?
You have to set up a "collector", or system to collect the RTCP XR reports from the devices. The reports are sent using SIP PUBLISH. To my knowledge, Asterisk does not have this capability.
You can use Opensips (SIP Proxy) and a database as a collector. http://wiki.sipfoundry.org/display/sipXecs/Setting+up+an+RTCP-XR+collector+for+Polycom+Productivity+Suite gives a general how-to on the way to do this.
I found it very difficult to get Opensips installed properly until I found a YouTube video showing me how. It was much easier once I found the video and watched him run through it.
I set up my Opensips on an Amazon EC2 micro instance with Ubuntu. The only modification had to make was to add the line advertised_address="x.x.x.x" (x.x.x.x being an elastic IP assigned to the instance) to the opensips.cfg file to deal with Amazon's one-for-one NAT arrangement. Opensips receives the SIP PUBLISH notifications and passes to a simple PERL script that writes the info to a database.