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An importance measure for multi-component systems with Semi-Markov dynamics

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider semi-Markov reliability models of multi-component systems with a discrete state space, general enough to include systems with maintenance or repair. We assume that for all system states the functioning or failure of each component is specified. In this setup we propose a component importance measure which is close in spirit to the classical steady state Barlow–Proschan importance measure for repairable binary coherent systems. We discuss our importance measure to some extent, highlighting the relation to the classical Barlow–Proschan measure, and present formulas expressing it in terms of quantities easily obtained from the building blocks of the semi-Markov process. Finally an example of a two-component cold standby system with maintenance and repair is presented which illustrates how our importance measure can be used in practical applications.
Rocznik
Strony
147--156
Opis fizyczny
Bibliogr. 17 poz., rys.
Twórcy
autor
  • Bundesamt für Strahlenschutz, Federal Office for Radiation Protection, Salzgitter, Germany
autor
  • Bundesamt für Strahlenschutz, Federal Office for Radiation Protection, Salzgitter, Germany
Bibliografia
  • [1] Barlow, R.E. & Proschan, F. (1965). Mathematical Theory of Reliability. SIAM Series in Appl. Math., Wiley, New York.
  • [2] Barlow, R.E. & Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Probability Models. Holt Rinehart and Winston, Inc., New York.
  • [3] Barlow, R.E. & Proschan, F. (1975). Importance of system components and fault tree events. Stoch. Proc. Appl. 3, 153-173.
  • [4] Boland, P. J. & El-Neweihi, E. (1995). Measures of component importance in reliability theory. Comput. Op. Res. 22, 455-463.
  • [5] Csenki, A. (1995). An integral equation approach to the interval reliability of systems modeled by finite semi-Markov processes. Reliab. Eng. Syst. Safety 47, 37-45.
  • [6] Csenki, A. (2007) Joint interval reliability for Markov systems with an application in transmission line reliability. Reliab. Eng. Syst. Safety 92, 685-696.
  • [7] Grabski, F. (2010). Semi-Markov reliability model of the cold standby system. J. Appl. Quant. Meth. 5, 486-496.
  • [8] Hellmich, M. & Berg, H.-P. (2012). Component importance for semi-Markov systems. Preprint.
  • [9] Huseby, A. B. (2004). Importance measures for multicomponent binary systems. Statist. Res. Report No. 11, Dept. of Math., Univ. of Oslo.
  • [10] Korolyuk, V.S., Brodi, S.M. & Turbin, A. F. (1975). Semi-Markov processes and their applications. J. Math. Sci. 4, 244-280.
  • [11] Limnios, N. & Oprisan, G. (2001). Semi-Markov Processes and Reliability. Birkhäuser, Boston.
  • [12] Natvig, B. & Gåsemyr, J. (2009). New results on the Barlow-Proschan and Natvig measures of component importance in nonrepairable and repairable systems. Methodol. Comput. Appl. Probab. 11, 603-620.
  • [13] Natvig, B. (2011). Measures of component importance in nonrepairable and repairable multistate systems. Methodol. Comput. Appl. Probab. 13, 523-547.
  • [14] Ouhbi, B. & Limnios, N. (2002). The rate of occurrence of failures for semi-Markov processes and estimation. Stat. Probab. Lett. 59, 245-255.
  • [15] Störmer, H. (1970). Semi-Markoff-Prozesse mit endlich vielen Zuständen: Theorie und Anwendungen. Springer Lecture Notes in Operations Research and Mathematical Systems Vol. 34, Berlin, Springer.
  • [16] Van, P.D. & Barros, A. (2008). Reliability importance analysis of Markovian systems at steady state using perturbation analysis. Reliab. Eng. Syst. Safety 93, 1605-1615.
  • [17] Veeramany, A. & Pandrey, D.P. Reliability analysis of nuclear piping system using semiMarkov process model. Reliab. Eng. Syst. Safety 38, 1133-1139.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-1c488fff-9aaf-417e-a8a2-5174808646d0
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