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System reliability analysis of a lamp problem by simulation

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Listed:
  • Zilong Feng
  • Tadashi Dohi
  • Won Young Yun

Abstract

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.

Suggested Citation

  • Zilong Feng & Tadashi Dohi & Won Young Yun, 2023. "System reliability analysis of a lamp problem by simulation," Journal of Risk and Reliability, , vol. 237(6), pages 1186-1198, December.
    • Handle: RePEc:sae:risrel:v:237:y:2023:i:6:p:1186-1198
    DOI: 10.1177/1748006X221116454
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    References listed on IDEAS

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    1. Hisashi Yamamoto & Tomoaki Akiba, 2005. "Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 243-252, April.
    2. Xin Feng & Alan T. Murray, 2018. "Allocation using a heterogeneous space Voronoi diagram," Journal of Geographical Systems, Springer, vol. 20(3), pages 207-226, July.
    3. Yamamoto, Hisashi & Akiba, Tomoaki & Nagatsuka, Hideki & Moriyama, Yurie, 2008. "Recursive algorithm for the reliability of a connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice system," European Journal of Operational Research, Elsevier, vol. 188(3), pages 854-864, August.
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