A production model with history based random machine failures

Knapp, Stephan ; Göttlich, Simone

DOI: https://doi.org/10.1007/978-3-030-27550-1_62
URL: https://link.springer.com/chapter/10.1007/978-3-03...
Document Type: Conference or workshop publication
Year of publication: 2019
Book title: Progress in Industrial Mathematics at ECMI 2018 : The 20th European Conference on Mathematics for Industry, 18-22 June 2018, Budapest, Hungary
The title of a journal, publication series: Mathematics in Industry
Volume: 30
Page range: 491-497
Conference title: ECMI 2018
Location of the conference venue: Budapest, Hungary
Date of the conference: 18.-22.06.2018
Publisher: Faragó, István
Place of publication: Cham
Publishing house: Springer
ISBN: 978-3-030-27549-5 , 978-3-030-27550-1
ISSN: 1612-3956 , 2198-3283
Publication language: English
Institution: School of Business Informatics and Mathematics > Wissenschaftliches Rechnen (Göttlich 2011-)
Subject: 510 Mathematics
Abstract: In this paper, we introduce a time-continuous production model that enables random machine failures, where the failure probability depends historically on the production itself. This bidirectional relationship between historical failure probabilities and production is mathematically modeled by the theory of piecewise deterministic Markov processes (PDMPs). On this way, the system is rewritten into a Markovian system such that classical results can be applied. In addition, we present a suitable solution, taken from machine reliability theory, to connect past production and the failure rate. Finally, we investigate the behavior of the presented model numerically in examples by considering sample means of relevant quantities and relative frequencies of number of repairs.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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ORCID: Knapp, Stephan ; Göttlich, Simone ORCID: 0000-0002-8512-4525

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