Joint Integrated Importance Measure for Multi-State Transition Systems

Abstract

Joint reliability importance (JRI) evaluates the interaction of two components in contributing to the system reliability in a system. Traditional JRI measures mainly concern the change of the system reliability caused by the interactive change of the reliabilities of the two components and seldom consider the probability distributions, transition rates of the object component states, and system performance. This article extends the JRI concept of two components from multi-state systems to multi-state transition systems and mainly focuses on the joint integrated importance measure (JIIM) which considers the transition rates of component states. Firstly, the concept and physical meaning of JIIM in binary systems are described. Secondly, the JIIM for deterioration process (JIIMDP) and the JIIM for maintenance process (JIIMMP) in multi-state systems are studied respectively. The corresponding characteristics of JIIMDP and JIIMMP for series and parallel systems are also analyzed. Finally, an application to an offshore electrical power generation system is given to demonstrate the proposed JIIM.

Keywords:

• Deterioration process
• Joint reliability importance
• Maintenance process
• Performance utility
• Reliability

Mathematics Subject Classification:

• 60K10
• 90B25

Acknowledgment

The authors gratefully acknowledge the financial support for this research from the 973 Program of China (Grant No. 2010CB328000), the National Natural Science Foundation of China (Grant No. 71101116), the Science and Technology Project of Shaanxi Province (Grant No. 2010K8-11), and the Grant of Northwestern Polytechnical University (No. 11GH0134).