Redundancy versus protection for a non-reparable phased-mission system subject to external impacts

Systems that have multiple consecutive and non-overlapping phases of operations during their missions are referred to as phased-mission systems (PMSs). Previous research on modeling reliability of a PMS has mainly focused on internal failures. However, some real-world PMSs can also be subject to external impacts, which may contribute to the occurrences of system failures. This paper makes contributions by modeling a redundant PMS subject to both internal failures and external impacts with or without overarching protection. System reliability is modeled for cases where the demand levels are the same for all phases, and where they are not. The optimal resource allocation of redundancy and protection is further studied to maximize the system reliability. The expected system loss is also modeled and optimized for cases where the system can function partially when the demand is unsatisfied. Examples are presented to illustrate applications of the proposed models.