The TS3500 internal web server provides some information about the
cartridges.  Not sure what they really means.
It does tell you the number of read and write errors for both LTO and
3592 cartridges from the cartridge memory.

Go to your TS3500 library internal web server
Expand +Cartridges
Select Data Cartridges
Select Download mount history(.csv)

This will pull up a spreadsheet with the last 100 mounts for the
library.

Information include are 

Mount History                                                           
                                                Mount   Life    >>>
                                                Tape Alert      Mounts
WRetries
                                                Media   Media   Media
Date and Time   VolSer  Frame   Drive   LogLib  EAddr   _1-64   Count
Count


                                                                        
>>>     >>>     >>>     Mount   >>>     >>>     >>>     >>>     >>>
>>>
WPerms  RRetries        RPerms  Rating  >>>     >>>     >>>     >>>
>>>     Write
Media   Media   Media   Drive   Media   Ports   Port0   Port1   Rsvd
Perf
Count   Count   Count   _1-255  _1-255  _1-255  _1-255  _1-255  _1-255
Util%

        

>>>     >>>     >>>     >>>     >>>     >>>     >>>     >>>     >>>
>>>     >>>     >>>
>>>     >>>     >>>     Read    >>>     >>>     >>>     Capacity
>>>     >>>     Crypto  >>>
ERPs    Burst   Buffer  Perf    ERPs    Burst   Buffer  Total   Writes
Control Status  Rekey
Impct%  Util%   Util%   Util%   Impct%  Util%   Util%   Util%   Util%
Util%