  A repairable threshold scheme (which we abbreviate to RTS) is a
$(\tau,n)$-threshold scheme in which a subset of players can "repair" another
player's share in the event that their share has been lost or corrupted. This
will take place without the participation of the dealer who set up the scheme.
The repairing protocol should not compromise the (unconditional) security of
the threshold scheme. Combinatorial repairable threshold schemes (or
combinatorial RTS) were recently introduced by Stinson and Wei. In these
schemes, "multiple shares" are distributed to each player, as defined by a
suitable combinatorial design called the distribution design. In this paper, we
study the reliability of these combinatorial repairable threshold schemes in a
setting where players may not be available to take part in a repair of a given
player's share. Using techniques from network reliability theory, we consider
the probability of existence of an available repair set, as well as the
expected number of available repair sets, for various types of distribution
designs.
