This article focuses on a toroidal connected-(r,s)-out-of-(m,n):F lattice system, which has m vertical circles and n horizontal circles, and the components are deployed at their intersections. This system fails if and only if the system has an sub-matrix where all components fail. It might be used to evaluate the reliability of a system with a toroidal structure, for example, toroidal storage tanks and neutron accelerators. The purpose of this article is to efficiently compute the reliability of the toroidal connected-(r,s)-out-of-(m,n):F lattice system. First, we propose a recursive method and then develop two kinds of algorithms based on this method. We apply an idea of preparing a set in a pre-processing phase to one algorithm, and consequently, the algorithm with the idea requires the extra memory space but has better time complexity compared with the other one. Finally, we investigate the efficiency of the two algorithms through numerical experiments.
BoehmeTKKossowAPreussW. A generalization of consecutive-k-out-of-n:F systems. IEEE T Reliab1992; 41(3): 451–457.
2.
YamamotoHMiyakawaM. Reliability of a linear connected-(r,s)-out-of-(m,n):F lattice system. IEEE T Reliab1995; 44(2): 333–336.
3.
ZhaoXCuiLZhaoW, et al. Exact reliability of a linear connected-(r,s)-out-of-(m,n):F system. IEEE T Reliab2011; 60(3): 689–698.
4.
YamamotoHMiyakawaM. Reliability of a circular connected-(r,s)-out-of-(m,n):F lattice system. J Oper Res Soc Jpn1996; 39(3): 389–406.
5.
YamamotoHAkibaT. A recursive algorithm for the reliability of a circular connected-(r,s)-out-of-(m,n):F lattice system. Comput Ind Eng2005; 49(1): 21–34.
6.
AkibaTNakamuraTXiaoX, et al. Evaluation methods for reliability of consecutive-k systems. In: RamMDohiT (eds) Systems engineering: reliability analysis using k-out-of-n structures. Boca Raton, FL: CRC Press, 2019, pp.1–24.
7.
RedekopDXuBZhangY. Stability of a toroidal fluid-containing shell. Int J Pres Ves Pip1999; 76(9): 575–581.
8.
TzouHWangD. Micro-sensing characteristics and modal voltages of linear/non-linear toroidal shells. J Sound Vib2002; 254(2): 203–218.
9.
NakamuraTYamamotoHShinzatoT, et al. Proposal of calculation method for reliability of toroidal connected-(1,2)-or-(2,1)-out-of-(m,n):F lattice system with Markov chain. In: NakamuraSQianCHNakagawaT (eds) Reliability modeling with computer and maintenance applications. Singapore: World Scientific, 2017, pp.139–153.
10.
KuoWZuoMJ. Optimal reliability modeling: principles and applications. Hoboken, NJ: John Wiley & Sons, 2003.
11.
LinCZengZZhouY, et al. A lower bound of reliability calculating method for lattice system with non-homogeneous components. Reliab Eng Syst Safe2019; 188: 36–46.
12.
ZhaoXZhaoWXieW. Two-dimensional linear connected-k system with trinary states and its reliability. J Syst Eng Electron2011; 22(5): 866–870.
