SSAS Cube for tracking changes in parent child relationship over time
Parent-child relationship in SSAS isn't straight forward as we might wish. From my experience in SSAS 2008 linking them both together wasn't simple at all.
In those type of cases the most recommended solution would be to flatten the relationship with a (SQL) view in which you link the parent to the child with the date attribute. That view becomes your dimension and on which you check the changes over time. 
you can find more data about this in here:
http://www.kimballgroup.com/2007/10/design-tip-95-patterns-to-avoid-when-modeling-headerline-item-transactions/
and here:
http://www.kimballgroup.com/2012/05/design-tip-145-time-stamping-accumulating-snapshot-fact-tables/
Alternatively:
If you need both the Parent id and the Child in the fact table (because you need to query on both) then in that case I would go on a different direction and include both id's in my fact table. This way you can monitor changes across time as you would for any other dimension.