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Failure profiles of coherent systems

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  • Félix Belzunce
  • Moshe Shaked

Abstract

In this paper we first introduce and study the notion of failure profiles which is based on the concepts of paths and cuts in system reliability. The relationship of failure profiles to two notions of component importance is highlighted, and an expression for the density function of the lifetime of a coherent system, with independent and not necessarily identical component lifetimes, is derived. We then demonstrate the way that failure profiles can be used to establish likelihood ratio orderings of lifetimes of two systems. Finally we use failure profiles to obtain bounds, in the likelihood ratio sense, on the lifetimes of coherent systems with independent and not necessarily identical component lifetimes. The bounds are relatively easy to compute and use. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • Félix Belzunce & Moshe Shaked, 2004. "Failure profiles of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 477-490, June.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:4:p:477-490
    DOI: 10.1002/nav.20010
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    References listed on IDEAS

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    1. Lillo, Rosa E. & Nanda, Asok K. & Shaked, Moshe, 2001. "Preservation of some likelihood ratio stochastic orders by order statistics," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 111-119, January.
    2. Josep Freixas & M. Puente, 2002. "Reliability Importance Measures of the Components in a System Based on Semivalues and Probabilistic Values," Annals of Operations Research, Springer, vol. 109(1), pages 331-342, January.
    3. Philip J. Boland & Taizhong Hu & Moshe Shaked & J. George Shanthikumar, 2002. "Stochastic Ordering of Order Statistics II," International Series in Operations Research & Management Science, in: Moshe Dror & Pierre L’Ecuyer & Ferenc Szidarovszky (ed.), Modeling Uncertainty, chapter 0, pages 607-623, Springer.
    4. Shanthikumar, J. George & Yao, David D., 1986. "The preservation of likelihood ratio ordering under convolution," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 259-267, December.
    5. Belzunce, Félix & Ruiz, José M. & Ruiz, M. Carmen, 2002. "On preservation of some shifted and proportional orders by systems," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 141-154, November.
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