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

Milczek B.

Journal of Polish Safety and Reliability Association

2018

Vol. 9, No. 3

115--120

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.

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

Milczek B.

Journal of Polish Safety and Reliability Association

2018

Vol. 9, No. 3

121--126

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].