  The growing size of the multiprocessor system increases its vulnerability to
component failures. It is crucial to locate and to replace the faulty
processors to maintain a system's high reliability. The fault diagnosis is the
process of identifying faulty processors in a system through testing. This
paper shows that the largest connected component of the survival graph contains
almost all remaining vertices in the $(n,k)$-arrangement graph $A_{n,k}$ when
the number of moved faulty vertices is up to twice or three times the
traditional connectivity. Based on this fault resiliency, we establishes that
the conditional diagnosability of $A_{n,k}$ under the comparison model. We
prove that for $k\geq 4$, $n\geq k+2$, the conditional diagnosability of
$A_{n,k}$ is $(3k-2)(n-k)-3$; the conditional diagnosability of $A_{n,n-1}$ is
$3n-7$ for $n\geq 5$.
