References
- Bai, G., Tian, Z. and Zuo, M.J. (2018) Reliability evaluation of multistate networks: An improved algorithm using state space decomposition and experimental comparison. IISE Transactions, (in press).
- De Figueiredo, L.H. and Stolfi, J. (2004) Affine arithmetic: Concepts and applications. Numerical Algorithms, 37(4), 147–158
- Destercke, S. and Sallak, M. (2013) An extension of universal generating function in multi-state systems considering epistemic uncertainties. IEEE Transactions on Reliability, 62(2), 504–514.
- Ding, Y. and Lisnianski, A. (2008) Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets and Systems, 159, 307–324.
- Ding, Y., Zuo, M., Lisnianski, A. and Li, W. (2010) A framework for reliability approximation of multi-state weighted k-out-of-n systems. IEEE Transactions on Reliability, 59, 297–308.
- Floudas, C. (2000) Deterministic Global Optimization: Theory, Algorithms and Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands.
- Kruse, R. and Meyer, K.D. (1987) Statistics with Vague Data, D. Reidel Publishing Company, Dordrecht, The Netherlands.
- Kwakernaak, H. (1978) Fuzzy random variables–I. Definitions and theorems, Information Sciences, 15(1), 1–29.
- 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(1), 323–330.
- Li, Y.F., Ding, Y. and Zio, E. (2014) Random fuzzy extension of the universal generating function approach for the reliability assessment of multi-state systems under aleatory and epistemic uncertainties. IEEE Transactions on Reliability, 63(1), 13–25.
- Lin, Y.H., Li, Y.F. and Zio, E. (2016) Reliability assessment of systems subject to dependent degradation processes and random shocks. IISE Transactions, 48 (11), 1072–1085.
- Lisnianski, A. and Levitin, G. (2003) Multi-State System Reliability: Assessment, Optimization and Applications, World Scientific, Singapore.
- Liu, Y. and Huang, H.Z. (2010) Reliability assessment for fuzzy multi-state systems. International Journal of Systems Science, 41(4), 365–379.
- Liu, Y., Huang, H.Z. and Levitin, G. (2008) Reliability and performance assessment for fuzzy multi-state elements. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 222(4), 675–686.
- Liuzzi, G., Lucidi, S. and Sciandrone, M. (2010) Sequential penalty derivative-free methods for nonlinear constrained optimization. SIAM Journal on Optimization, 20(5), 2614–2635.
- Martinez, F.A., Sallak, M. and Schön, W. (2015) An efficient method for reliability analysis of systems under epistemic uncertainty using belief function theory. IEEE Transactions on Reliability, 64(3), 893–909.
- Mi, J., Li, Y.F., Liu, Y., Yang, Y.J. and Huang, H.Z. (2015) Belief universal generating function analysis of multi-state systems under epistemic uncertainty and common cause failures. IEEE Transactions on Reliability, 64(4), 1300–1309.
- Natvig, B. (2011) Multistate System Reliability Theory With Applications, Wiley, New York, NY.
- Perez, R.E., Jansen, P.W. and Martins, J.R.R.A. (2011) pyOpt: A Python-based object-oriented framework for nonlinear constrained optimization. Structures and Multidisciplinary Optimization, 45(1), 101–118.
- Sallak, M., Schön, W. and Aguirre, F. (2013) Reliability assessment for multi-state systems under uncertainties based on the Dempster-Shafer theory. IIE Transactions, 45(9), 995–1007.
- Shen, J. and Cui, L. (2017) Reliability performance for dynamic multi-state repairable systems with K regimes. IISE Transactions, 49(9), 911–926.
- Sun, M.X., Li, Y.F. and Zio, E. (2018) On the optimal redundancy allocation for multi-state series C parallel systems under epistemic uncertainty. Reliability Engineering & System Safety, (in press).
- Wang, Y. and Li, L. (2012) Effects of uncertainty in both component reliability and load demand on multi-state system reliability. IEEE Transactions on Systems, Man and Cybernetics–Part A, 42, 958–969.
- Wang, Y., Li, L., Huang, S. and Chang, Q. (2012) Reliability and covariance estimation of weighted k-out-of-n multi-state systems. European Journal of Operational Research, 221, 138–147.
- Yeh, W.C. (2017) Methodology for the reliability evaluation of the novel learning-effect multi-state flow network. IISE Transactions, 49 (11), 1078–1085.