Modeling reliability of systems with repair by stochastic processes with long memory

• Autorzy: Filus Jerzy K. , Filus Lidia Z.

Identyfikatory

DOI

10.26408/srsp-2023-06

• Konferencja: 17th Summer Safety & Reliability Seminars - SSARS 2023, 9-14 July 2023, Kraków, Poland
• Języki publikacji: EN

Abstrakty

EN

In modelling reliability of systems with repair by stochastic processes of times between consecutive failures the usual Markovianity assumption was significantly relaxed. Instead of the Markovian stochastic processes, processes with long memory were constructed for the reliability and maintenance applications. The Markovianity restriction on the process’s memory could be omitted as two (relatively) new methods of the processes construction were employed. In this work, one of the two available methods, the ‘method of triangular transformations’, is presented. Other, the ‘method of parameter dependence’, is shortly described in Section 5. Since using an arbitrarily long memory has serious drawbacks in modelling process we, on the other hand, limited it by introducing the notion of k-Markovianity (k = 1,2,…), where the memory is reduced to the last k previous (discrete) time epochs. The discussion of this kind of problems together with construction of some new classes of stochastic processes with discrete time and their reliability application is provided.

Słowa kluczowe

EN

discrete time; unlimited memory stochastic processes; k-Markovianity; triangular transformations; method of parameter dependence

• Wydawca: Gdynia Maritime University ; Polskie Towarzystwo Bezpieczeństwa i Niezawodności
• Czasopismo: Safety and Reliability of Systems and Processes
• Rocznik: 2023
• Tom: Summer Safety and Reliability Seminar 2023
• Strony: 69--78
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Filus Jerzy K.

• Oakton College, Des Plaines, U.S.A.

• https://orcid.org/0000-0002-5083-5626

autor

Filus Lidia Z.

• Northeastern Illinois University, Chicago, U.S.A.

• https://orcid.org/0000-0002-4267-5773

Bibliografia

• Filus, J. & Filus, L. 1999. A class of generalized multivariate normal densities (revisited), Report, No. 99-1109, Northeastern Illinois University, Chicago.
• Filus, J. & Filus, L. 2001. On some bivariate pseudonormal densities. Pakistan Journal of Statistics 17(1), 1-19.
• Filus, J. & Filus, L. 2008. Construction of new continuous stochastic processes. Pakistan Journal of Statistics 24(3), 227-251.
• Filus, J., Filus, L. & Arnold, B. 2010. Families of multivariate distributions involving triangular transformations. Communications in Statistics - Theory and Methods 39(1), 107-116.
• Filus, J. & Filus, L. 2013. A method for multivariate probability distributions construction via parameter dependence. Communications in Statistics: Theory and Methods 42(4), 716-721.
• Kotz, S., Balakrishnan, N. & Johnson, N. 2000. Continuous Multivariate Distributions, Volume 1: Models and Applications, A Wiley-Interscience Publication, John Wiley & Sons, INC, Second Edition, New York - Chichester - Weinheim - Brisbane - Singapore - Toronto.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).