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Identifying optimal components in a reliability system Freixas Bosch, Josep Pons Vallès, Montserrat Àrees temàtiques de la UPC::Matemàtiques i estadística Reliability (Engineering) Birnbaum’s measure of reliability importance important components pre-ordering relation Fiabilitat (Enginyeria) The first step in a reliability optimization process is to make a reliability assessment for each component in the system. If this assessment is made in a qualitative way, by grouping together components with the same reliability, and establishing a prevalence order among groups, is there a way to decide which components have the greatest Birnbaum measure without computing the exact value of this measure? In this paper, three relations between com- ponents are introduced and studied, and it is proved that they are useful for selecting the components that have the biggest effect on the system reliability in the sense of Birnbaum. An algorithm that uses the results in the paper to select these important components is also provided. Peer Reviewed Postprint (published version) 2008-03 Article https://www.cs.tcd.ie/disciplines/statistics/statica/statica_web/GDRR13/GDRR13_Programme_files/Freixas_associatedpaper.pdf Open Access Institute of Electrical and Electronics Engineers (IEEE)