The paper proposes a simulation-based procedure to determine the system reliability of a lamp problem. Suppose we have k lamps to light up a room, and each lamp can light a circular area of radius r. The system reliability is the probability that there is no dark area in the room during time t. We obtain the system reliability function and the expected system lifetime through a simulation when the reliability and the coverage radius of the lamps are given. A Monte Carlo test method and an Intersection test method are used to check the system state (working or failure) for different situations. In numerical examples, Kaplan–Meier and Nelson estimators determine the system reliability function from system failure times generated by the simulation. Additionally, we compare the two methods with numerical examples.
ErikssonHErikssonKSjöstrandJ.Note on the lamp lighting problem. Adv Appl Math2001; 27(2–3): 357–366.
2.
ZhouZDasSGuptaH.Connected K-coverage problem in sensor networks. In: 13th International Conference on computer communications and networks ICCCN 2004 (IEEE Cat. No. 04EX969) Chicago, USA, 11-13 October 2004, pp. 373-378. New York: IEEE.
3.
HuangCFTsengYC.The coverage problem in a wireless sensor network. Mob Netw Appl2005; 10(4): 519–528.
4.
ChengCFWangCW.The target-barrier coverage problem in wireless sensor networks. IEEE Trans Mob Comput2018; 17(5): 1216–1232.
5.
SalviaAALasherWC.Two-dimensional consecutive-k-out-of-n:F models. IEEE Trans Reliab1990; 39(3): 382–385.
6.
ZuoM.Reliability and design of 2-Dimensional consecutive-k-out-of-n Systems. IEEE Trans Reliab1993; 42(3): 488–490.
7.
YamamotoHMiyakawaM.Reliability of a linear Connected-(r,s)-out-of-(m,n):F Lattice System. IEEE Trans Reliab1995; 44(2): 333–336.
8.
MalinowskiJPreussW.Lower and upper bounds for the reliability of Connected-(r,s)-out-of-(m,n):F lattice systems. IEEE Trans Reliab1996; 45(1): 156–160.
9.
YamamotoH.Reliability of a connected-(r1, s1)-or-(r2, s2)-or-..-or-(rk, sk)-out-of-(m,n): F lattice system. Microelectron Reliab1996; 36(2): 151–168.
10.
YamamotoHAkibaTNagatsukaH, et al. Recursive algorithm for the reliability of a connected-(1,2)-or-(2,1)-out-of-(m,n):F lattice system. Eur J Oper Res2008; 188(3): 854–864.
11.
YamamotoHAkibaT.Evaluating methods for the reliability of a large 2-dimensional rectangular k-within-consecutive-(r,s)-out-of-(m,n):F system. Nav Res Logist2005; 52(3): 243–252.
12.
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.
13.
ZuoMJWuY.Reliability Evaluation of Combined k-out-of-n:F, consecutive-k-out-of-n:F and linear connected-(r, s)-out-of-(m, n):F System Structures. IEEE Trans Reliab2000; 49(1): 99–104.
14.
HigashiyamaY.A recursive method for computing the reliability of circular consecutive 2-out-of-(m, n): F system. Int J Reliab Qual Saf Eng2002; 09(03): 229–235.
15.
ZhaoXCuiLZhaoW, et al. Exact reliability of a linear connected-(r,s)-out-of-(m,n): F system. IEEE Trans Reliab2011; 60(3): 689–698.
16.
GuoJLiuZCheH, et al. Reliability model of consecutive (2, k) -out-of-( 2, n ) :F systems with local load-sharing. IEEE Access2018; 6: 8178–8188.
17.
NakamuraTYamamotoHAkibaT.Reliability of a toroidal connected-(r,s)-out-of-(m,n):F lattice system. Proc IMechE, Part O: J Risk and Reliability2022; 236: 329–338.
18.
LiuQ.KK-barier coverage reliability evaluation for wireless sensor networks using two-dimensional k-within-consecutive-r × s-out-of-m × n:F system. Proc IMechE, Part O: J Risk and Reliability2019; 233(6): 1029–1039.
19.
LiuQ.Coverage reliability evaluation of wireless sensor network considering common cause failures based on d–s evidence theory. IEEE Trans Reliab2021; 70(1): 331–345.
20.
FengXMurrayAT.Allocation using a heterogeneous space Voronoi diagram. J Geogr Syst2018; 20(3): 207–226.
21.
DreznerZKalczynskiPSalhiS.The planar multiple obnoxious facilities location problem: A Voronoi based heuristic. Omega2019; 87: 105–116.
22.
OkabeABootsBSugiharaK, et al. Spatial tessellations: Concepts and applications of Voronoi diagrams. 2nd ed. Hoboken, NJ: Wiley, 2000.
23.
SuzukiADreznerZ.The P-center location problem in an area. Location Sci1996; 4(1-2): 69–82.
