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The (k+1)-th component of linear consecutive–k–out–of–n systems

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Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 32))

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Abstract

A linear consecutive–k–out–of–n:F system is an ordered sequence of n components that fails if and only if at least k consecutive components fail. A linear consecutive–k–out–of–n:G system is an ordered sequence of n components that works if and only if at least k consecutive components work.

The existing necessary conditions for the optimal design of systems with 2k ≤ n provide comparisons between reliabilities of components restricted to positions from 1 to k and positions from n to (n - k + 1). This chapter establishes necessary conditions for the variant optimal design that involve components at some other positions, including component (k+1). Procedures to improve designs not satisfying those conditions are also given.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Tasmania, Hobart, TAS 7001, Australia

    Małgorzata O’Reilly

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  1. Małgorzata O’Reilly
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    © 2009 Springer-Verlag New York

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    O’Reilly, M. (2009). The (k+1)-th component of linear consecutive–k–out–of–n systems. In: Pearce, C., Hunt, E. (eds) Optimization. Springer Optimization and Its Applications, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-0-387-98096-6_17

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