  It is often difficult for a phased mission system (PMS) to be highly
reliable, because this entails achieving high reliability in every phase of
operation. Consequently, reliability analysis of such systems is of critical
importance. However, efficient and interpretable analysis of PMSs enabling
general component lifetime distributions, arbitrary structures, and the
possibility that components skip phases has been an open problem.
  In this paper, we show that the survival signature can be used for
reliability analysis of PMSs with similar types of component in each phase,
providing an alternative to the existing limited approaches in the literature.
We then develop new methodology addressing the full range of challenges above.
The new method retains the attractive survival signature property of separating
the system structure from the component lifetime distributions, simplifying
computation, insight into, and inference for system reliability.
