If the work process are going to PRIV mode this means that the Extend Memory is exhausted.
As you are running AIX, probably have set the parameter ES/TABLE = SHM_SEGS. Therefore the Extend Memory is controlled by the parameter EM/TOTAL_SIZE_MB.
See note 445533.
The area limited by the parameter EM/TOTAL_SIZE_MB is shared between all work process. Each individual work process can grow individually in the Extend Memory until the limit of ztta/roll_extension.
Basicaly:
EM/TOTAL_SIZE_MB = Total of EM to all Work Process;
ztta/roll_extension = limit of EM of an individual WP;
To avoid the PRIV mode you should increase the Extend Memory. You only need to check if you have to increase the individual work process extend memory area (ztta/roll_extension) or the total area.
It is possible to check the EM utilization in ST02 transaction. Click twice in the Extend Memory and you see something
Extended memory Dialog session kB 97.656
Nondialog sess. kB 97.656
Available kB 4.190.208
Used kB 122.880
Maximum used kB 237.568
If the Maximum used reach the size of EM/TOTAL_SIZE_MB this means that the bottleneck is in the area shared by all work process.
Best regards
Clebio Dossa