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Open AccessArticle

Locating Arrays with Mixed Alphabet Sizes

1
School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
2
Graduate School of Information Science and Technology, Osaka University, Suita 565-0871, Japan
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 831; https://doi.org/10.3390/math8050831
Received: 29 April 2020 / Revised: 15 May 2020 / Accepted: 18 May 2020 / Published: 20 May 2020
(This article belongs to the Section Mathematics and Computer Science)
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. View Full-Text
Keywords: combinatorial testing; locating arrays; lower bound; construction; mixed orthogonal arrays combinatorial testing; locating arrays; lower bound; construction; mixed orthogonal arrays
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Shi, C.; Jin, H.; Tsuchiya, T. Locating Arrays with Mixed Alphabet Sizes. Mathematics 2020, 8, 831.

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