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On the construction of component importance measures for semi-Markov systems

Published on Feb 1, 2013in Mathematical Methods of Operations Research1.023
· DOI :10.1007/s00186-012-0413-6
Mario Hellmich5
Estimated H-index: 5
,
Heinz-Peter Berg1
Estimated H-index: 1
Abstract
In this paper we consider semi-Markov reliability models of systems with discrete state space in a setup general enough to cover systems with maintenance and repair. The systems are assumed to consist of several components which can either be up or down in each state. In this framework we propose two different types of component importance measures which are based on transition rates and interval availability, respectively. For these importance measures we study both the time-dependent and the steady state situation, and express them in terms of quantities easily calculated from the building blocks of the semi-Markov process.
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  • Citations (1)
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In Natvig and Gasemyr (Methodol Comput Appl Probab 11:603–620, 2009) dynamic and stationary measures of importance of a component in a binary system were considered. To arrive at explicit results the performance processes of the components were assumed to be independent and the system to be coherent. Especially the Barlow–Proschan and the Natvig measures were treated in detail and a series of new results and approaches were given. For the case of components not undergoing repair it was shown tha...
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