Phased mission systems (PMSs) appear in many areas of science and technology. A PMS accomplishes its mission in multiple non-overlapping consecutive phases. The system may perform different tasks in the phases under different success criteria, configurations, and environmental situations. In this article, we consider a PMS with components having three states: complete performance, partial performance, and complete failure. The reliability of the system is explored under two different scenarios. The first case is about the PMS with similar components in the phases and the latter one is on the PMS which may have multiple types of components in the phases. To this, in each case, a new version of survival signature is defined for the system which depends only on the system structure and is free of the random mechanism of components failure. Then, under these circumstances, some compact expressions are given for the PMS reliability in which the structure of PMS is separated from the reliability functions of the components. The results are generalized to the PMSs with multi-state components. Some examples and a real practical system are given to illustrate the proposed models.
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