Cathode deterioration is a very quirky process, quite nonlinear, and to test you need to place the tube under load. Those old tube testers Sparky described did a much better job than the last of the breed (the dime-store testers). Dynamic testers (the equivalent of a transistor curve tracer, another thing you rarely see outside a fab or specialized test house these days) have pretty much faded away except for very specialized applications (I bet ARC has a few!)
I have a few gov't reports in my files, but they are buried deep in the pseudo-tame black hole masquerading as a basement storage room... There were some tube handbooks from companies like RCA that held a wealth of "lost knowledge". I just reached over to grab mine, but that shelf is now filled with woodworking books (another fun, expensive hobby for which I have no time
). Undoubtedly now a victim of that durn black hole. There is quite a bit of info on tubes in several textbooks from various undergrad and grad classes I took way back when, and my
Reference Data for Radio Engineers handbook (Sams/ITT, 5th ed, was a bright shiny replacement for my old one when I first bought it back in the 70's) has a lot of information about tubes and tube circuits.