Measuring availability from CAP theorem
This is indeed a concern for those building real-world applications - how does one measure "availability" - not the binary property discussed in the CAP theorem, but the experience for users of the system.

There is industry agreement around this concern, and a standardized method of measuring it applicable to all systems. (Note: as stated in the comments, this is a separate concept from the theoretical concept of availability, which is analyzed from an algorithm, or perhaps from a simulation of a system.)

The Apdex method assumes you have a definition of "satisfied service" at some response time. Let's say you consider a sub-1-second response time to satisfactory to define "available." Then, by convention, "tolerable" service is 4 times the target time: in our case, a response time from 1 to 4 seconds. Response times longer than 4 seconds are considered "frustrated." 

Then, the Apdex score is the number of satisfied requests, plus half the number of tolerable requests, plus none of the frustrated requests (i.e. 0), all divided by the total number of requests. 

For example, if you had 100 total requests, and 30 of them were satisfied (&lt; 1s), 50 were tolerable (>1s but &lt;4s) and 20 were frustrated (>4s), the apdex score for your service for the period of time those requests were serviced would be (30+25+0)/100, or 0.55. (An apdex score, by virtue of being a ratio, is always between 0 and 1) 

Fun fact: a bunch of businesses then teamed up to turn this quite simple idea into a fully-fledged business. If you are a business, you can pay the Apdex Alliance money so they can produce education, webinars, and blogs, as well as certify compliant business so they may use the Apdex name and logo(!)

(I am not affiliated with the Alliance. I just like standards.)