Abstract :
To identify the critical components or sets of components in a system, various importance measures have been proposed with different probabilistic perspectives and applications. Many of these importance measures are actually related to each other in some ways. This paper summarizes the importance measures in reliability, and presents relations and comparisons among them, focusing on their interrelations to the B-importance, the dominant relations among them, the dual relations, their performances in typical systems, and their computations. The early versions of the importance measures are for binary coherent systems, while the recent research is not limited to this type of system. This paper investigates the extensions of importance measures in noncoherent systems, multistate systems, continuum systems, and repairable systems.
Keywords :
duality (mathematics); probability; reliability theory; set theory; B-importance measures; binary coherent systems; continuum systems; critical component set identification; dominant relations; dual relations; multistate systems; noncoherent systems; probabilistic perspectives; reliability; repairable systems; Joints; Position measurement; Probabilistic logic; Redundancy; Time measurement; Vectors; Continuum systems; importance measures; multi state systems; noncoherent systems; repairable systems;
