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1

Safety of some homogeneous series-„k out of n” systems

Milczek B.

Journal of Polish Safety and Reliability Association

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2018

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Vol. 9, No. 3

115--120

EN

In the reliability investigation of large-scale systems, the problem of the complexity of their safety functions arises. This problem may be approximately solved by assuming that the number of system components tends to infinity and finding the limit safety function of the system. The problem of finding the limit reliability function of large-scale systems is well known for basic two-state systems (Gnedenko for series and parallel systems [1], Smirnov for “k out of n” systems [8]). The problem of possible limit reliability functions for series-parallel and parallel-series is also well recognized [3]. The solution for two-state series-“k out of n” systems, while k/n→0 and also while k/n→1 can be found in [5] and [6]. The paper is concerned with mathematical methods in multistate asymptotic approach to series-“k out of n” systems safety and shows the methods of establishing its possible limit safety functions, while k/n→ λ, 0˂ λ˂ 1.

2

Safety of multistate series-„k out of n” systems

Milczek B.

Journal of Polish Safety and Reliability Association

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2018

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Vol. 9, No. 3

121--126

EN

The paper is concerned with mathematical methods in asymptotic approach to systems safety and reliability analysis. In the safety investigation of large-scale systems, the problem of the complexity of their safety functions arises. This problem may be approximately solved by assuming that the number of system components tends to infinity and finding the limit safety function of the system. The article is based on the results of the author’s solutions for series-“m out of kn” given in [4] – [6].

3

On a few reliability issues in telecommunication networks

Tanguy C.

Journal of Polish Safety and Reliability Association

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2010

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Vol. 1, No. 1

239--246

EN

The paper proposes a short survey on a few issues currently addressed in telecommunication networks. We show on an example that the k-terminal reliability of recursive families of graphs can also be expressed in terms of products of matrices, leading to a simple asymptotic result. The uncertainty on equipment failure rates, which are not always easy to assess, and the possible occurrence of common-cause failures combine to possibly make the overall connection availability and failure frequency different from their expected values assuming independent failures. We finally discuss a source of impairment in long-haul optical networks, and other current issues where improvements would lead to a reduction of costs and to a better quality of service.

4

Asymptotic approach to reliability evaluation of piping and rope transportation systems.

Kołowrocki K.

Zagadnienia Eksploatacji Maszyn

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2000

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Vol. 35, nr 2

111-133

EN

Limit reliability functions of large multistate systems applications to reliability and risk evaluation of piping and rope transportation systems are presented in the paper.

PL

W artykule przedstawione są zastosowania granicznych funkcji niezawodności dużych systemów wielostanowych do oszacowania niezawodności i ryzyka systemów transportu rurociągowego i linowego.

5

O niezawodności i ryzyku dużych systemów wielostanowych ze starzejącymi się elementami.

Kołowrocki K.

Zagadnienia Eksploatacji Maszyn

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1999

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Vol. 34, nr 2

189-210

PL

W artykule przedstawione są klasy możliwych granicznych funkcji niezawodności dla dowolnych jednorodnych wielostanowych systemów szeregowych, równoległych, szeregowo-równoległych oraz równoległo-szeregowych. Ponadto przedstawione są zastosowania uzyskanych wyników do oszacowania niezawodności tych systemów oraz ich funkcji ryzyka.

EN

In the paper the classes of limit reliability functions for homogeneous multistate series, parallel, series-parallel and parallel-series systems are presented. Moreover, some applications of the achieved results to the reliability evaluation and the risk assessment of the considered system are given.