A production model with history based random machine failures


Knapp, Stephan ; Göttlich, Simone


URL: https://arxiv.org/abs/1901.10260
Document Type: Conference or workshop publication
Year of publication: 2019
Book title: The 20th European Conference on Mathematics for Industry 18-22 June 2018, Budapest, Hungary : proceedings
Page range: tba
Conference title: ECMI 2018
Location of the conference venue: Budapest, Hungary
Date of the conference: 18-22 June 2018
Place of publication: Cham
Publishing house: Springer
ISBN: tba
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.

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Knapp, Stephan ; Göttlich, Simone ORCID: 0000-0002-8512-4525 A production model with history based random machine failures. tba In: The 20th European Conference on Mathematics for Industry 18-22 June 2018, Budapest, Hungary : proceedings (2019) Cham ECMI 2018 (Budapest, Hungary) [Conference or workshop publication]


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

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