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

• Autorzy: Milczek B.
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

large systems; safety of large systems; asymptotic approach; limit reliability function

• Wydawca: Polskie Towarzystwo Bezpieczeństwa i Niezawodności
• Czasopismo: Journal of Polish Safety and Reliability Association
• Rocznik: 2018
• Tom: Vol. 9, No. 3
• Strony: 115--120
• Opis fizyczny: Bibliogr. 9 poz., rys., tab., wykr.

Twórcy

autor

Milczek B.

• Maritime University, Gdynia, Poland

Bibliografia

• [1] Gnedenko B. V. (1943) Sur la Distribution Limité du Terme Maximum d’une Serie Aleatoire. Ann. of Math. 44, 432-453.
• [2] Kolowrocki K. (1993). On a Class of Limit Reliability Functions for Series-Parallel and Parallel-Series Systems. Monograph. Maritime University Press, Gdynia.
• [3] Kolowrocki K. (2004). Reliability of Large Systems. Elsevier, Amsterdam - Boston - Heidelberg - London - New York - Oxford - Paris - San Diego - San Francisco - Singapore - Sydney - Tokyo.
• [4] Kołowrocki, K. & Soszyńska-Budny, J. (2011). Reliability and Safety of Complex Technical Systems and Processes: Modeling - Identification - Prediction - Optimization, London, Dordrecht, Heildeberg, New York, Springer.
• [5] Milczek B. (2002). On The Class of Limit Reliability Functions of Homogeneous Series“k-out-of-n” Systems. Applied Mathematics and Computation 137, 161-174.
• [6] Milczek B. (2004). Limit Reliability Functions of Some Series-“k out of n” Systems, International Journal Of Materials & Structural Reliability, Vol. 2 No 1, 1-11.
• [7] Milczek B. (2004). Limit Reliability Functions of Series-“k-out-of-n” Systems, Ph.D. thesis, Department of Mathematics, Maritime University, Gdynia.
• [8] Smirnov N. V. (1949). Predelnye Zakony Raspredelenya Dla Chlenov Varyatsyonnogo Ryada. Trudy Matem. Inst. im. V. A. Stelkova.
• [9] Soszyńska J. (2006). Reliability evaluation of a port oil transportation system in variable operation conditions. International Journal of Pressure Vessels and Piping, Vol. 83, Issue 4, 304-310.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).