On a class of limit reliability functions of some regular homogeneous series-parallel systems

• Autorzy: Kołowrocki Krzysztof

Identyfikatory

DOI

10.14708/ma.v22i36.1816

• Języki publikacji: EN

Abstrakty

EN

In the investigation of large-scale systems the problem of the complexity of their reliability functions arises. This problem may be solved approximately by assuming that the number of system components tends to infinity and finding the limit reliability function. In this paper a four-element class of limit reliability functions for a regular homogeneous series-parallel system is presented. The number of series components of the system has the order of the logarithm of the number of its parallel components. The result is obtained under the assumption that the lifetimes of the particular components are independent and identically distributed random variables. The class presented is different from the known class of limit distributions of minimax statistics of independent random variables with the same distribution. Moreover, some examples of the systems considered and their limit reliability functions are given. The results can be useful in the investigation of the reliability of large systems.

Słowa kluczowe

EN

reliability; life testing

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Matematyka Stosowana : matematyka dla społeczeństwa
• Rocznik: 1993
• Tom: Nr 36
• Strony: 55--69
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kołowrocki Krzysztof

• Katedra Matematyki, Wyższa szkoła Morska, ul. Morska 83, 81-962 Gdynia, Polska

Bibliografia

• [1] R. E. Barlow and P. Proschan, Statistical Theory of Reliability and Life Testing. Probability Models, Holt, Rinehart and Winston, New York, 1975.
• [2] H. Chernoff and H. Teicher, Limit distributions of the minimax of independent identically distributed random variables, Proc. Amer. Math. Soc. 116 (1965), 174-491.
• [3] L. de Haan, On regular variation and its application to the weak convergence of sample extremes, Matj. Center. Tracts 32, Amsterdam, 1970.
• [4] K. Kołowrocki, On a class of limit reliability functions of some regular homogeneous series-parallel systems. Reliability Engineering and System Safety 39, No 1 (1993), 11-23, Elsevier.
• [5] K. Kołowrocki. Limit reliability functions of some series-parallel and parallel-series systems. Applied Mathematics and Computation, Elsevier (in press).
• [6] K. Kołowrocki. On a class of limit reliability functions for series-parallel and parallel-series systems, monograph, 125 pp., Wydawnictwo WSM w Gdyni, 1993.
• [7] B. Kopociński, Zarys teorii odnowy i niezawodności, PWN, Warszawa, 1973.