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Locating Arrays with Mixed Alphabet Sizes

Author

Listed:
  • Ce Shi

    (School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China)

  • Hao Jin

    (Graduate School of Information Science and Technology, Osaka University, Suita 565-0871, Japan)

  • Tatsuhiro Tsuchiya

    (Graduate School of Information Science and Technology, Osaka University, Suita 565-0871, Japan)

Abstract

Locating arrays (LAs) can be used to detect and identify interaction faults among factors in a component-based system. The optimality and constructions of LAs with a single fault have been investigated extensively under the assumption that all the factors have the same values. However, in real life, different factors in a system have different numbers of possible values. Thus, it is necessary for LAs to satisfy such requirements. We herein establish a general lower bound on the size of mixed-level ( 1 ¯ , t ) -locating arrays. Some methods for constructing LAs including direct and recursive constructions are provided. In particular, constructions that produce optimal LAs satisfying the lower bound are described. Additionally, some series of optimal LAs satisfying the lower bound are presented.

Suggested Citation

  • Ce Shi & Hao Jin & Tatsuhiro Tsuchiya, 2020. "Locating Arrays with Mixed Alphabet Sizes," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:831-:d:360744
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    References listed on IDEAS

    as
    1. Charles J. Colbourn & Daniel W. McClary, 2008. "Locating and detecting arrays for interaction faults," Journal of Combinatorial Optimization, Springer, vol. 15(1), pages 17-48, January.
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