It really depends on the server specs and how both instances are accessed.

Without knowing any details except that the server is running a production SQL instance, I would recommend putting Analysis Services on a different server.

The two possible benefits of running Analysis Services on the same server as SQL:

1. You can use Shared Memory net library for better performance. (bypasses the physical network stack)

2. Lower hardware costs.

The benefit of Shared Memory only matters during processing since this is the only time the Analysis Service connects to the SQL instance.

The risks you face with having them on a shared server comes with resource contention and scalability.