RELIABILITY ANALYSIS OF MULTI-STATE COMPLEX SYSTEM HAVING TWO MULTI-STATE SUBSYSTEMS UNDER UNCERTAINTY
Keywords:
Multi-State System, Consecutive r-out of-k-from-n System, Interval Universal Generating Function, Reliability, MTTF.Abstract
n this paper a non-repairable multi-state complex system with two subsystems A and B is taken for study. The subsystems A and B are multi-state consecutive r-out-of-k-from-n: G systems connected in parallel configuration. Analysis of the system reliability is carried out incorporating the uncertainty in the probabilities and degradation rates of the subsystem elements. The uncertainty representation in probabilities and degradation rates is done by their interval values. The probability intervals are evaluated by computing bound of interval valued ordinary differential equation of the system. Interval universal generating function is used to obtain reliability and mean time to failure of the proposed system. Finally, the considered model is demonstrated with the help of a numerical example.
Downloads
References
Barlow, R. and Wu, A. (1978). Coherent systems with multi-state elements,
Mathematics of Operations Research, 3, p. 275–281.
Desterche, S. and Sallak, M. (2013). An extension of universal generating
function in multi-state system considering epistemic uncertainties, IEEE
Transactions on Reliability, 62(2), p. 504-514.
Ding, Y. and Lisnianski, A. (2008). Fuzzy universal generating functions for
multi-state system reliability assessment, Fuzzy Sets and Systems, 159(3), p.
-324.
El-Neveihi, E., Prochan, F. and Setharaman (1978). Multi-state coherent
systems, Journal of Applied Probability, 15, p. 675-688.
Habib, A., Al-Seedy, R. O. and Radwan, T. (2007). Reliability evaluation of
multi-state consecutive k-out-of-r-from-n: G system, Applied Mathematical
Modelling, 31(11), p. 2412-2423.
Meenakshi and Singh, S.B. (2016). Availability assessment of multi-state
system by hybrid universal generating function and probability intervals,
International Journal of Performability Engineering, 4, p. 321-339.
Levitin, G. (2005). Reliability of linear multistate multiple sliding window
systems, Nav. Res. Log., 52 (3), p. 212-223.
Levitin, G. and Lisnianski, A. (1999). Importance and sensitivity analysis of
multi state systems using the universal generating function method, Reliability
Engineering & System Safety, 65(3), p. 271-282.
Levitin, G. and Xing, L. (2010). Reliability and performance of multi state
systems with propagated failures having selective effect, Reliability
Engineering & System Safety, 95(6), p. 655–661.
Levitin, G. (2005). The Universal Generating Function in Reliability Analysis
and Optimization, London: Springer-Verlag.
Li, C.-Y., Chen, X., Yi, X.-S. and Tao, J.-Y. (2011). Interval-valued reliability
analysis of multi-state systems, IEEE Transactions on Reliability, 60, p. 323 -
Lisnianski, A. (2007). Extended block diagram method for a multi-state
system reliability assessment, Reliability Engineering & System Safety,
(12), p. 1601-1607.
Lisnianski, A. and Levitin, G. (2003). Multi-State System Reliability:
Assessment, Optimization and Applications, World Scientific Publishing Co.
Pte. Ltd.
Marquez, J. R. and Coit, D. (2005). A Monte-Carlo simulation approach for
approximating multi-state two-terminal reliability, Reliability Engineering &
System Safety, 87(2), p. 253–264.
Papastavridis, S. and Koutras, M. V. (1993). Bounds for reliability of
consecutive-k-within-m-out-of-n systems, IEEE Trans. Reliability, R-42, p.
–160.
Papastavridis, S. and Sfakianak, M. E. (1991). Optimal arrangement and
importance of the components in a consecutive-k-out-of-r-from-n: F system,
IEEE Trans. Reliability, R-40, p. 277–279.
Pourret, O., Collet, J. and Bon, J. L. (1999). Evaluation of the unavailability of
a multi-state component system using a binary model, Reliability Engineering
& System Safety, 64(1), p. 13-17.
Ramdani, N., Meslem, N. and Candau, Y. (2010). Computing reachable sets
for uncertain nonlinear monotone systems, Nonlinear Analysis: Hybrid
System, 4, p. 263-278.
Sfakianakis, M., Kounias, S. and Hillaris, A. (1992). Reliability of a
consecutive-k-out-of-r-from-n: F system, IEEE Trans. Reliability, R-41, p.
-447.
Simon, C. and Weber, P. (2009). Evidential networks for reliability analysis
and performance evaluation of systems with imprecise knowledge. IEEE
Transactions on Reliability, 58(1), p. 69–87.
Tong, Y.L. (1985). Rearrangement inequality for the longest run with an
application to network reliability, J. Appl. Prob., 22, p. 286-393.
Xiao, N.-C., Huang, H.-Z., Liu, Y., Li, Y. and Wang, Z. (2012). Unified
uncertainty analysis by the extension universal generating functions. in
International Conference on Quality, Reliability, Risk, Maintenance, and
Safety Engineering (ICQR2MSE), p. 1160 -1166.
Xue, J. and Yang, K. (1995). Dynamic reliability analysis of coherent
multistate systems, IEEE Transactions on Reliability, 44, p. 253–264.
Zio, E., Marella, M. and Podofillini, L. (2007). A Monte Carlo simulation
approach to the availability assessment of multi-state systems with operational
dependencies, Reliability Engineering & System Safety, 92(7), p. 871-882.
