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.