  We present exact calculations of reliability polynomials $R(G,p)$ for lattice
strips $G$ of fixed widths $L_y \le 4$ and arbitrarily great length $L_x$ with
various boundary conditions. We introduce the notion of a reliability per
vertex, $r(\{G\},p) = \lim_{|V| \to \infty} R(G,p)^{1/|V|}$ where $|V|$ denotes
the number of vertices in $G$ and $\{G\}$ denotes the formal limit $\lim_{|V|
\to \infty} G$. We calculate this exactly for various families of graphs. We
also study the zeros of $R(G,p)$ in the complex $p$ plane and determine exactly
the asymptotic accumulation set of these zeros ${\cal B}$, across which
$r(\{G\})$ is nonanalytic.
