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Joint integrated importance measure for multi-state transition systems. (English) Zbl 1284.90018

The paper extends some classical concepts regarding the measure of the interaction (importance) of a pair of components in a coherent system in reliability. Thus, by combining the integrated importance measure (IIM) and the joint reliability importance (JRI) notions, the authors introduce the joint integrated importance measure (JIIM) concept. Firstly, this new concept is commented and studied for binary systems. Then, the JIIM is discussed in multi-state systems. In this frame, JIIM is adapted for the deterioration processes (JIIMDP) and for the maintenance processes (JIIMMP), respectively. Some characteristics of the JIIM for these kind of processes are presented. Finally, a case study refers to the comparison between these new concepts and some related known concepts.

MSC:

90B25 Reliability, availability, maintenance, inspection in operations research
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62N05 Reliability and life testing
62P30 Applications of statistics in engineering and industry; control charts
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