An effective way of improving the reliability of a system is the
allocation of active redundancy. Let $X_{1}$, $X_{2}$ be independent
lifetimes of the components $C_{1}$ and $C_{2}$, respectively, which
form a series system. Let denote $U_{1} = \min ( \max
An effective way of improving the reliability of a system is the
allocation of active redundancy. Let $X_{1}$, $X_{2}$ be independent
lifetimes of the components $C_{1}$ and $C_{2}$, respectively, which
form a series system. Let denote $U_{1} = \min ( \max
(X_{1},X),X_{2})$ and $U_{2} = \min (X_{1},\max (X_{2},X))$, where X
is the lifetime of a redundancy (say S) independent of $X_{1}$ and
$X_{2}$. That is $U_{1}(U_{2})$ denote the lifetime of a system
obtained by allocating S to $C_{1}(C_{2})$ as an active redundancy.
Singh and Misra (1994) considered the criterion where $C_{1}$ is
preferred to $C_{2}$ for redundancy allocation if $P(U_{1}
> U_{2})\geq P(U_{2} > U_{1})$. In this paper we use the same
criterion of Singh and Misra (1994) and we investigate the
allocation of one active redundancy when it differs depending on the
component with which it is to be allocated. We find sufficient
conditions for the optimization which depend on the components and
redundancies probability distributions. We also compare the
allocation of two active redundancies (say $S_{1}$ and $S_{2}$) in
two different ways, that is $S_{1}$ with $C_{1}$ and $S_{2}$ with
$C_{2}$ and viceversa. For this case the hazard rate order plays an
important role. We obtain results for the allocation of more than
two active redundancies to a k-out-of-n systems.[+][-]