Size of OBDD representation of 2-level redundancies functions

We consider an explicit boolean function depending on n = (i + 1) j variables encoding 2-level cascade redundancies in critical systems. We establish lower and upper bounds on the size of its OBDD representation. The exact lower bound of this function is comprised between (2min( i 2 ; j 2 )) and O(2min(i;j)). The upper bound is (2i(j 2log2i)). We further show that, when one of the parameters i or j is constant, this function admits OBDDs whose size is polynomial in other parameter. The latter result is constructive, and we show variable orderings that witness this polynomial size.