  We consider the mobile robot dispersion problem in the presence of faulty
robots (crash-fault). Mobile robot dispersion consists of $k\leq n$ robots in
an $n$-node anonymous graph. The goal is to ensure that regardless of the
initial placement of the robots over the nodes, the final configuration
consists of having at most one robot at each node. In a crash-fault setting, up
to $f \leq k$ robots may fail by crashing arbitrarily and subsequently lose all
the information stored at the robots, rendering them unable to communicate. In
this paper, we solve the dispersion problem in a crash-fault setting by
considering two different initial configurations: i) the rooted configuration,
and ii) the arbitrary configuration. In the rooted case, all robots are placed
together at a single node at the start. The arbitrary configuration is a
general configuration (a.k.a. arbitrary configuration in the literature) where
the robots are placed in some $l<k$ clusters arbitrarily across the graph. For
the first case, we develop an algorithm solving dispersion in the presence of
faulty robots in $O(k^2)$ rounds, which improves over the previous
$O(f\cdot\text{min}(m,k\Delta))$-round result by \cite{PS021}. For the
arbitrary configuration, we present an algorithm solving dispersion in
$O((f+l)\cdot\text{min}(m, k \Delta, k^2))$ rounds, when the number of edges
$m$ and the maximum degree $\Delta$ of the graph is known to the robots.
