  We present a coupled decreasing sequence of random walks on $ \mathbb Z $
that dominates the edge process of oriented-bond percolation in two dimensions.
Using the concept of "random walk in a strip ", we construct an algorithm that
generates an increasing sequence of lower bounds that converges to the critical
probability of oriented-bond percolation. Numerical calculations of the first
ten lower bounds thereby generated lead to an improved,i.e. higher, rigorous
lower bound to this critical probability, viz. $p_{c} \geq 0.63328 $. Finally a
computer simulation technique is presented; the use thereof establishes 0.64450
as a non-rigorous five-digit-precision (lower) estimate for $p_{c}$.
