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Multivariate stochastic comparisons of inspection and repair policies

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  • Hu, Taizhong
  • Wei, Ying

Abstract

For a system consisting of n independent components, inspection and repair policies are compared in the sense of the usual multivariate stochastic order with respect to the partial orderings [greater-or-equal, slanted]b1 and [greater-or-equal, slanted]b2 on the set of permutations of {1,...,n}. A given permutation [pi] of {1,...,n} determines the order in which components are visited and inspected. We assume that the reliability of the ith component is given by Pi, where P1[less-than-or-equals, slant]P2[less-than-or-equals, slant]...[less-than-or-equals, slant]Pn. If [pi] and [pi]' are two permutations such that [pi][greater-or-equal, slanted]b1[pi]', we show that inspecting the system with [pi] is better than with [pi]' in the sense that more failed components are encountered or less time is used in completing an inspection. If each component is made up of t parts assembled in parallel, it is shown that, for three types of repair policies, the rank of preference of inspection procedures is consistent with the partial ordering [greater-or-equal, slanted]b2 on the permutations. Our main results strengthen those in Boland, El-Neweihi and Proschan (Ann. Appl. Probab. 1 (1991) 207).

Suggested Citation

  • Hu, Taizhong & Wei, Ying, 2001. "Multivariate stochastic comparisons of inspection and repair policies," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 315-324, June.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:3:p:315-324
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    References listed on IDEAS

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    1. Takemi Yanagimoto & Masashi Okamoto, 1969. "Partial orderings of permutations and monotonicity of a rank correlation statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 489-506, December.
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