  It is known that the ordered Bell numbers count all the ordered partitions of
the set $[n]=\{1,2,\dots,n\}$. In this paper, we introduce the deranged Bell
numbers that count the total number of deranged partitions of $[n]$. We first
study the classical properties of these numbers (generating function, explicit
formula, convolutions, etc.), we then present an asymptotic behavior of the
deranged Bell numbers. Finally, we give some brief results for their
$r$-versions.
