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Locating and detecting arrays for interaction faults

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  • Charles J. Colbourn

    (Arizona State University)

  • Daniel W. McClary

    (Arizona State University)

Abstract

The identification of interaction faults in component-based systems has focused on indicating the presence of faults, rather than their location and magnitude. While this is a valuable step in screening a system for interaction faults prior to its release, it provides little information to assist in the correction of such faults. Consequently tests to reveal the location of interaction faults are of interest. The problem of nonadaptive location of interaction faults is formalized under the hypothesis that the system contains (at most) some number d of faults, each involving (at most) some number t of interacting factors. Restrictions on the number and size of the putative faults lead to numerous variants of the basic problem. The relationships between this class of problems and interaction testing using covering arrays to indicate the presence of faults, designed experiments to measure and model faults, and combinatorial group testing to locate faults in a more general testing scenario, are all examined. While each has some definite similarities with the fault location problems for component-based systems, each has some striking differences as well. In this paper, we formulate the combinatorial problems for locating and detecting arrays to undertake interaction fault location. Necessary conditions for existence are established, and using a close connection to covering arrays, asymptotic bounds on the size of minimal locating and detecting arrays are established.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:15:y:2008:i:1:d:10.1007_s10878-007-9082-4
    DOI: 10.1007/s10878-007-9082-4
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    References listed on IDEAS

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    1. Søren Bisgaard, 1996. "A Comparative Analysis of the Performance of Taguchi's Linear Graphs for the Design of Two‐Level Fractional Factorials," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(3), pages 311-322, September.
    2. Subir Ghosh & Colleen Burns, 2002. "Theory & Methods: Comparison of Four New General Classes of Search Designs," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(3), pages 357-366, September.
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    Cited by:

    1. Ce Shi & Hao Jin & Tatsuhiro Tsuchiya, 2020. "Locating Arrays with Mixed Alphabet Sizes," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    2. Ryan E. Dougherty & Kristoffer Kleine & Michael Wagner & Charles J. Colbourn & Dimitris E. Simos, 2023. "Algorithmic methods for covering arrays of higher index," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-21, January.

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