A NEW APPROACH TO DETERMINATION OF THE MOST CRITICAL MULTI-STATE COMPONENTS IN MULTI-STATE SYSTEMS
Abstract
A new approach to determination of the most critical multi-state components in multi-state systems is presented. The approach is based on solving an appropriate reliability optimization problem. The consideration is restricted on coherent and homogenous systems. Multi-state components may have different and distinct states which vary from complete failure to perfect functionality. The number of possible states is fixed and the same for all components and the system as a whole. The states correspond to different performance levels of components and the system. It is supposed that for each component state the corresponding probability and cost is known and that a higher state implies a higher cost. Further on, it is supposed that states of components are mutual statistically independent random variables. An original mathematical model for reliability calculation is developed and a corresponding optimization problem for identifying the most critical components is formulated and solved on numerical example.
References
Barlow, R.E, Wu, A.S (1978) Coherent Systems with Multi-State Components. Mathematics of Operations Research, Vol. 3, No. 4, 275-281;
Birnbaum, Z.W. (1969) On the importance of different components in a multicomponent system. In Multivariate Analysis, 2 (ed. Krishnaiah PR), Academic Press, New York. 581–592;
Crhistofides, N, Korman, S (1975) A computational survey of methods for the set covering problem, Management Science, 21, 591–599;
Ericson II, C.A (2005) Hazard Analysis technique for System Safety, John Wiley & Sons, New Jersey;
Kuo, W, Zhu, X (2012) Importance measures in reliability, risk, and optimization, John Wiley&Sons, Chichester;
Kvassay, M, Zaitseva, E, Levasheko, V (2015) Minimal ut stes and direct partial logic derivates in reliability analysis. In Nowakowski et al. Safety and Reliability: Methodology and Appliation, Taylor & Francis Group, London, 241-248;
Levitin G, Lisnianski A (1999) Importance and sensitivity analysis of multi-state systems using the universal generating function method. Reliability Engineering and System Safety 65, 271–282;
Levitin, G, Podofillini, L, Zio, E (2003) Generalised importance measures for multi-state elements based on performance level restrictions. Reliability Engineering and System Safety 82, 287–298;
Limnios, N. (2007) Fault Тree. ISTE Ltd, Wiltshire;
Lisnianski, A., Frenkel, I., & Ding, Y. (2010). Multi-state system reliability analysis and optimization for engineers and industrial managers. Springer Science & Business Media;
Ramirez-Marquez, Coit, D.W (2007) Multi-state component criticality analysis for reliability improvement in multi-state systems. Reliability Engineering and System Safety 94, 1608-1619;
Ramirez-Marquez, J. E, Rocco, C.M, Gebre, B.A, Coit, D.W, Tortorella, M (2006) New insights on multi-state component criticality and importance. Reliability Engineering and System Safety 91, 894–904;
Vesely, W.E, Davis, T.C, Denning, R.S, Saltos, N. (1983) Measures of risk importance and their applications, Battelle Columbus Labs., OH (USA).
Xie M, Dai, Y-S, Poh, K-L (2004) Computing System Reliability, Models and Analysis, Kluwer Academic Publishers, New York;
Yingkui, G, Jing, L (2012) Multi-State System Reliability: A New and Systematic Review. Procedia Engineering 29, 531-536;
Zaitseva, E (2012) Importance Analysis of a Multi-State System Based on Multiple-Valued Logic Methods. Chapter 8 in A. Lisnianski and I. Frenkel (eds.), Recent Advances in System Reliability, Springer Series in Reliability Engineering, Springer-Verlag, London, 113-134;
Zio E. (2009) Reliability engineering: Old problems and new challenges. Reliability Engineering and System Safety 94, 125–141;
Zio E. (2011) Risk importance measures. In:PhamH,editor. Safety and Risk Modeling and its Applications. London:Springer, 151–196.
