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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
Content available Safety of multistate series-„k out of n” systems
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
Content available Reliability of large three-dimensional nanosystems
EN
Basic notions and agreements on reliability of three-dimensional nanosystems are introduced. The asymptotic approach to the three-dimensional nanosystem reliability investigation is presented and the nanosystem limit reliability function is defined. Auxiliary theorems on limit reliability functions of three-dimensional nanosystems composed of large number of independent nanocomponents are formulated and the classes of limit reliability functions for a homogeneous series and series-parallel nanosystems are fixed. A model of a three-dimensional series and series-parallel nanosystem with dependent nanocomponents is created and the class of limit reliability functions identical with the class in the previous case is fixed as well. The asymptotic approach to reliability evaluation of exemplary three-dimensonal series and series-parallel nanosystem with dependent nanocomponents is presented and its accuracy is discussed.
EN
The paper deals with analysis of ships operation states in open water areas effected by environmental constraints influencing on ship sea keeping parameters in application to “Stena Baltica” ferry operated at the Baltic Sea between Gdynia and Karlskrona harbors.
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.
6
Content available Reliability modelling of complex systems. Part 2
EN
Series-“m out of n” systems and “m out of n”-series systems are defined and exemplary theorems on their limit reliability functions are presented and applied to the reliability evaluation of a piping transportation system and a rope elevator. Applications of the asymptotic approach in large series systems reliability improvement are also presented. The paper is completed by showing the possibility of applying the asymptotic approach to the reliability analysis of large systems placed in their variable operation processes. In this scope, the asymptotic approach to reliability evaluation for a port grain transportation system related to its operation process is performed.
7
Content available Reliability modelling of complex systems. Part 1
EN
The paper is concerned with the application of limit reliability functions to the reliability evaluation of large systems. Two-state large non-repaired systems composed of independent components are considered. The asymptotic approach to the system reliability investigation and the system limit reliability function are defined. Two-state homogeneous series, parallel and series-parallel systems are defined and their exact reliability functions are determined. The classes of limit reliability functions of these systems are presented. The results of the investigation concerned with domains of attraction for the limit reliability functions of the considered systems and the investigation concerned with the reliability of large hierarchical systems as well are discussed in the paper. The paper contains exemplary applications of the presented facts to the reliability evaluation of large technical systems.
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