A Semi-Markov Model with Geometric Renewal Processes
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| Název: | A Semi-Markov Model with Geometric Renewal Processes |
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| Autoři: | Zhang, Jingqi, Fouladirad, Mitra, Limnios, Nikolaos |
| Přispěvatelé: | Laboratoire Modélisation et Sûreté des Systèmes (LM2S), Laboratoire Informatique et Société Numérique (LIST3N), Université de Technologie de Troyes (UTT)-Université de Technologie de Troyes (UTT), Aix Marseille Université (AMU), Laboratoire de Mécanique, Modélisation et Procédés Propres (M2P2), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Appliquées de Compiègne (LMAC), Université de Technologie de Compiègne (UTC) |
| Zdroj: | ISSN: 1387-5841. |
| Informace o vydavateli: | CCSD Springer Verlag |
| Rok vydání: | 2023 |
| Témata: | Semi-Markov process, Geometric process, Reliability, semi-Markov process geometric process reliability, [INFO]Computer Science [cs], [MATH]Mathematics [math] |
| Popis: | International audience ; We consider a repairable system modeled by a semi-Markov process (SMP), where we include a geometric renewal process for system degradation upon repair, and replacement strategies for non-repairable failure or upon N repairs. First Pérez-Ocón and Torres-Castro studied this system (Pérez-Ocón and Torres-Castro in Appl Stoch Model Bus Ind 18(2):157–170, 2002) and proposed availability calculation using the Laplace Transform. In our work, we consider an extended state space for up and down times separately. This allows us to leverage the standard theory for SMP to obtain all reliability related measurements such as reliability, availability (point and steady-state), mean times and rate of occurrence of failures of the system with general initial law. We proceed with a convolution algebra, which allows us to obtain final closed form formulas for the above measurements. Finally, numerical examples are given to illustrate the methodology. |
| Druh dokumentu: | article in journal/newspaper |
| Jazyk: | English |
| DOI: | 10.1007/s11009-023-10060-z |
| Dostupnost: | https://utt.hal.science/hal-04543367 https://utt.hal.science/hal-04543367v1/document https://utt.hal.science/hal-04543367v1/file/v1_covered_045c7e17-ebb2-4ee9-bb26-38612ece18c9.pdf https://doi.org/10.1007/s11009-023-10060-z |
| Rights: | info:eu-repo/semantics/OpenAccess |
| Přístupové číslo: | edsbas.7055F25F |
| Databáze: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | International audience ; We consider a repairable system modeled by a semi-Markov process (SMP), where we include a geometric renewal process for system degradation upon repair, and replacement strategies for non-repairable failure or upon N repairs. First Pérez-Ocón and Torres-Castro studied this system (Pérez-Ocón and Torres-Castro in Appl Stoch Model Bus Ind 18(2):157–170, 2002) and proposed availability calculation using the Laplace Transform. In our work, we consider an extended state space for up and down times separately. This allows us to leverage the standard theory for SMP to obtain all reliability related measurements such as reliability, availability (point and steady-state), mean times and rate of occurrence of failures of the system with general initial law. We proceed with a convolution algebra, which allows us to obtain final closed form formulas for the above measurements. Finally, numerical examples are given to illustrate the methodology. |
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| DOI: | 10.1007/s11009-023-10060-z |