Reliability analysis of multi-state phased-mission systems

Multi-state phased-mission systems (MS-PMS) are multi-state systems that are subject to multiple, consecutive, and non-overlapping phases of operation. The challenges in analyzing MS-PMS are mainly due to the s-dependence across different phases and among different states of a given component; as well as the dynamic system configuration, failure criteria, and component failure behavior in different phases. Existing methods for the reliability analysis of MS-PMS are either based on monolithic Markov models that suffer from the well-known state explosion problem, or use a hierarchical strategy that facilitates the modeling of components with multiple states, but still classifies the component states into binary states at the system level. In this paper, we propose a hierarchical modeling approach that integrates an efficient multi-valued decision diagram model for representing the system structure function at the upper level and Markov models for describing components' behaviors at the lower level. The proposed approach can overcome the limitations of the existing methods and is applicable to MS-PMS with both ordered and unordered component states. The application and advantages of the proposed approach are illustrated through a case study in which the reliability for a sequence of tasks in a multi-state Grid system will be analyzed.