HP-UX uses initscripts to start processes. So you need an initscript which includes commands to start, stop, and check status of processes.
Let's take the Arbiter; it's a standalone process at OS level and is easier:
The Arbiter is an instance of ISCAgent, whose initscript is likely at /sbin/init.d/ISCAgent on your HP-UX system.
Symlink to that script in the runlevel directory for the runlevels you need this to run; this should be /sbin/rc3.d for runlevel 3 or /sbin/rc4.d for runlevel 4. You can review the HP-UX runlevels by reading the manpage for init (1M) (the command man init should get you there).
In those directories, you'll see names starting with S##name and K##name (digits for the #). This signals which services are (S)tarted or (K)illed when the system switches to this runlevel. On my test machine here, in /sbin/rc3.d I see S900ISCAgent, and I can see that it would start after
You would need a similar initscript which would start Cache'. I would expect that the Arbiter would be run on a host distinct from its mirror members. You can review the ISCAgent initscript to get a sense of how these are organized.