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Application of the stein‐chen method for bounds and limit theorems in the reliability of coherent structures

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  • Markos V. Koutras
  • Stavros G. Papastavridis

Abstract

The Stein‐Chen method for establishing Poisson convergence is used to approximate the reliability of coherent systems with exponential‐type distribution functions. These bounds lead to quite general limit theorems for the lifetime distribution of large coherent systems. © 1993 John Wiley & Sons, Inc.

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  • Markos V. Koutras & Stavros G. Papastavridis, 1993. "Application of the stein‐chen method for bounds and limit theorems in the reliability of coherent structures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 617-631, August.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:5:p:617-631
    DOI: 10.1002/1520-6750(199308)40:53.0.CO;2-4
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    References listed on IDEAS

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    1. Mingjian Zuo & Way Kuo, 1990. "Design and performance analysis of consecutive‐K‐out‐of‐n structure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(2), pages 203-230, April.
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    1. Koutras, M. V. & Papastavridis, S. G. & Petakos, K. I., 1996. "Bounds for coherent reliability structures," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 285-292, February.
    2. John A. Steele & Gábor J. Székely, 2004. "Limiting survival functions of self‐similar structures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 155-165, March.
    3. 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.
    4. James C. Fu & W. Y. Wendy Lou, 2007. "On the Normal Approximation for the Distribution of the Number of Simple or Compound Patterns in a Random Sequence of Multi-state Trials," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 195-205, June.

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