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Compound poisson approximation in systems reliability

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  • A. D. Barbour
  • Ourania Chryssaphinou
  • Malgorzata Roos

Abstract

The compound Poisson “local” formulation of the Stein‐Chen method is applied to problems in reliability theory. Bounds for the accuracy of the approximation of the reliability by an appropriate compound Poisson distribution are derived under fairly general conditions, and are applied to consecutive‐2 and connected‐s systems, and the 2‐dimensional consecutive‐k‐out‐ofn system, together with a pipeline model. The approximations are usually better than the Poisson “local” approach would give. © 1996 John Wiley & Sons, Inc.

Suggested Citation

  • A. D. Barbour & Ourania Chryssaphinou & Malgorzata Roos, 1996. "Compound poisson approximation in systems reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 251-264, March.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:2:p:251-264
    DOI: 10.1002/(SICI)1520-6750(199603)43:23.0.CO;2-9
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    References listed on IDEAS

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    1. James Fu & Markos Koutras, 1994. "Poisson approximations for 2-dimensional patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 179-192, March.
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    Cited by:

    1. Joseph Glaz & Marco Guerriero & Rohini Sen, 2010. "Approximations for a Three Dimensional Scan Statistic," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 731-747, December.
    2. 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.
    3. Anant P. Godbole & Laura K. Potter & Jessica K. Sklar, 1998. "Improved upper bounds for the reliability of d‐dimensional consecutive‐k‐out‐of‐n : F systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(2), pages 219-230, March.

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