IA POSIX compatible OS is usually a derivative of UNIX.
Not quite.
POSIX is a programming
standard which I think originated in Unix systems but is by no means Unix specific. It's usually used becasue it's required in systems that the US government use.
Completely non-Unix OSs can also be POSIX compliant (to a greater or lesser degree).
e.g. Windows NT, BeOS, QNX.