What I understand from your question is that you want to measure the user experience based on technical terms, i.e.: number of views for a specific page, number of error pages showed to users, how many times a link has been clicked, what locations the users come from all over the world, and so on.
So, I think you are asking about website analytics, which you custom to do measurements for whatever you want, as famous examples for those tools:
- Splunk
- Google Analytics
- Open Web Analytics (open source)
Please let me know if I answered your question.