2008/09/08 by Alexander Dukhovny, Dukhovny, Alexander, Jean‐Luc Marichal +2
Decision Sciences · Engineering · Mathematics · #62N05 #90B25 (Primary) 28B15 #94C10 (Secondary) #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Probabilistic and Robust Engineering Design #Probability (math.PR) #Rings and Algebras (math.RA) #math.PR #math.RA #msc:28B15 #msc:62N05 #msc:90B25 #msc:94C10
paper · pdf · doi:10.48550/arxiv.0809.1332
19 pages
arxiv created 2008/09/08 · openalex publication_date 2008/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A semicoherent system can be described by its structure function or, equivalently, by a lattice polynomial function expressing the system lifetime in terms of the component lifetimes. In this paper we point out the parallelism between the two descriptions and use the natural connection of lattice polynomial functions and relevant random events to collect exact formulas for the system reliability. We also discuss the equivalence between calculating the reliability of semicoherent systems and calculating the distribution function of a lattice polynomial function of random variables.