Several eoneepts of importance measures have been proposed and used in system engineering, based on different views of the influence of the components on the system performance. The standard definitions of importance measures hold for binary components in binary systems (i.e., the components, as well as the whole system can only stay in two states: working or failed). However, a multi-state modelling of components and systems is often required in practice. In this paper, the most frequently used importance measures are generalized to the case of multi-state systems made of multi-state components. The introduced extensions characterize the importance of a component achieving its different possible levels of performance with respect to the overall mean multi-state unavailability. The work is methodological in nature. An illustrative example is provided with regards to a simple multi-state system.
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