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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

Correlation and regression analysis of winter experimental statistical data of the operation process of the Stena Baltica ferry

Habibullah M. S., Xiuju F., Kołowrocki K., Soszyńska J., Milczek B.

Problemy Eksploatacji

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2009

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nr 4

135-151

EN

These are presented statistical methods of correlation and regression analysis of the operation processes of complex technical systems. The collected statistical data from the Stena Baltica ferry operation process are analysed and used for determining correlation coefficients and single and multiple regression equations, expressing the influence of the operation process conditional sojourn times in particular operation states on the operation process total time.

PL

Przedstawione są statystyczne metody analizy regresji i korelacji procesów eksploatacji złożonych systemów technicznych. Zebrane dane statystyczne z procesu eksploatacji promu Stena Baltica zostały zanalizowane i użyte do wyznaczenia współczynnika korelacji oraz do wyznaczenia równań jednokrotnej i wielokrotnej regresji, wyrażającej wpływ warunkowych czasów przebywania procesu eksploatacji w poszczególnych stanach eksploatacyjnych na całkowity czas procesu eksploatacji.

4

Examples of series-“m out of k” systems and their limit reliability functions

Milczek B.

Journal of Polish Safety and Reliability Association

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2009

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Vol. 2

309--316

EN

The paper is concerned with mathematical methods in asymptotic approach to systems reliability analysis. The complexity of the reliability investigation of large-scale systems is proposed to be approximately solved by assuming that the number of system components tends to infinity and finding the limit reliability function of the system. Some general results in the form of auxiliary theorems and examples of limit reliability functions of homogeneous and regular series-“m out of k” systems with exponential and Weibull reliability functions of system components are presented.