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Reliability bounds for multistage structures with independent components

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  • Kordecki, Wojciech

Abstract

In this note, the lower bound and the upper bound on the reliability of a coherent multistage system are considered for independent components. The main tool used to obtain these bounds is the theory of Markov chains on lattices of structure states. Such a reliability structure is described as a family of convex sets. Numerical examples show the relationships between the bounds presented in this paper and the bounds obtained by Fu and Koutras (1995) for bridge structure and for structures derived from a projective plane of rank 2.

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  • Kordecki, Wojciech, 1997. "Reliability bounds for multistage structures with independent components," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 43-51, May.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:1:p:43-51
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    References listed on IDEAS

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    1. Fu, J. C. & Koutras, M. V., 1995. "Reliability bounds for coherent structures with independent components," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 137-148, February.
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    Cited by:

    1. Kim-Hung Li & Cheuk Ting Li, 2019. "Linear Combination of Independent Exponential Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 253-277, March.
    2. Anindya S. Chakrabarti, 2011. "Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics," Papers 1112.2168, arXiv.org.
    3. Agazzi, Andrea & Andreis, Luisa & Patterson, Robert I.A. & Renger, D.R. Michiel, 2022. "Large deviations for Markov jump processes with uniformly diminishing rates," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 533-559.

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