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Reliability Approximation for Markov Chain Imbeddable Systems

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  • Michael V. Boutsikas

    (University of Piraeus)

  • Markos V. Koutras

    (University of Piraeus)

Abstract

In the present article, a simple method is developed for approximating the reliability of Markov chain imbeddable systems. The approximating formula reduces the problem to the reliability assessment of smaller systems with structure similar to the original systems. Two specific reliability structures which have attracted considerable research interest recently (r-within-consecutive-k-out-of-n system and two dimensional r-within-k 1 × k 2-out-of-n 1 × n 2 system) are studied by the new approach and numerical calculations are carried out, which reveal the high quality of our approximations. Several possible extensions and generalizations are also presented in brief.

Suggested Citation

  • Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.
    • Handle: RePEc:spr:metcap:v:2:y:2000:i:4:d:10.1023_a:1010062218369
    DOI: 10.1023/A:1010062218369
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    References listed on IDEAS

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    Cited by:

    1. Alexandru Amarioarei & Cristian Preda, 2020. "One Dimensional Discrete Scan Statistics for Dependent Models and Some Related Problems," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    2. Dafnis, Spiros D. & Makri, Frosso S. & Philippou, Andreas N., 2019. "The reliability of a generalized consecutive system," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 186-193.
    3. Qianzhu Wu & Joseph Glaz, 2019. "Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 295-314, March.
    4. Qianzhu Wu & Joseph Glaz, 2021. "Scan Statistics for Normal Data with Outliers," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 429-458, March.
    5. 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.
    6. Morteza Ebneshahrashoob & Tangan Gao & Mengnien Wu, 2005. "An Efficient Algorithm for Exact Distribution of Discrete Scan Statistics," Methodology and Computing in Applied Probability, Springer, vol. 7(4), pages 459-471, December.

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