  The concept of joint bivariate signature, introduced by Navarro et al.
(2013), is a useful tool for quantifying the reliability of two systems with
shared components. As with the univariate system signature, introduced by
Samaniego (2007), its applications are limited to systems with only one type of
components, which restricts its practical use. Coolen and Coolen-Maturi (2012)
introduced the survival signature, which generalizes Samaniego's signature and
can be used for systems with multiple types of components. This paper
introduces a joint survival signature for multiple systems with multiple types
of components and with some components shared between systems. A particularly
important feature is that the functioning of these systems can be considered at
different times, enabling computation of relevant conditional probabilities
with regard to a system's functioning conditional on the status of another
system with which it shares components. Several opportunities for practical
application and related challenges for further development of the presented
concept are briefly discussed, setting out an important direction for future
research.
