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Consecutive Detecting Arrays for Interaction Faults

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Abstract

The concept of detecting arrays was developed to locate and detect interaction faults arising between the factors in a component-based system during software testing. In this paper, we propose a family of consecutive detecting arrays (CDAs) in which the interactions between factors are considered to be ordered. CDAs can be used to generate test suites for locating and detecting interaction faults between neighboring factors. We establish a general criterion for measuring the optimality of CDAs in terms of their size. Based on this optimality criterion, the equivalence between optimum CDAs and consecutive orthogonal arrays with prescribed properties is explored. Using the advantages of this equivalence, a great number of optimum CDAs are presented. In particular, the existence of optimum CDAs with few factors is completely determined.

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments that much improved both the quality and readability of this paper. Our research is supported by Natural Science Foundation of China under Grant 11301342 and Natural Science Foundation of Shanghai under Grant 17ZR1419900.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, China

    Ce Shi

  2. College of Information Technology, Shanghai Ocean University, Shanghai, 201306, China

    Ling Jiang

  3. School of International Economics and Trade, Shanghai Lixin University of Accounting and Finance, Shanghai, 201209, China

    Aiyuan Tao

Authors
  1. Ce Shi
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  2. Ling Jiang
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  3. Aiyuan Tao
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Correspondence to Aiyuan Tao.

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Appendix

Appendix

A simple \(\hbox {COA}_\lambda (2,5,6)\) with \(\lambda =3 \) or 5 is given below.

\(\lambda =3\), \(A=(A_1,A_2)^T\), where \(A_1\) and \(A_2\) are as follows.

$$\begin{aligned} A_1= & {} \left( \begin{array}{c} 000000000000000000111111111111111111222222222222222222\\ 000111222333444555000111222333444555000111222333444555\\ 013023245145035124245145013023124035013023245145035124\\ 453154032210025134201023541345314205501205413324430215\\ 111111111111111111222222222222222222333333333333333333 \end{array} \right) \\ A_2= & {} \left( \begin{array}{c} 333333333333333333444444444444444444555555555555555555\\ 000111222333444555000111222333444555000111222333444555\\ 245145013023124035013023245145035124245145013023124035\\ 342431052150125340042340521135514320153512403204230154\\ 444444444444444444555555555555555555000000000000000000 \end{array} \right) \end{aligned}$$

\(\lambda =5\), \(B=(B_1,B_2,B_3)^T\), where \(B_1\), \(B_2\) and \(B_3\) are as follows.

$$\begin{aligned} B_1= & {} \left( \begin{array}{c} 000000000000000000000000000000111111111111111111111111111111\\ 000001111122222333334444455555000001111122222333334444455555\\ 012340123501245013450234512345012450123401345012351234502345\\ 012341234523450345014501250123103522145032415435204012351034\\ 111111111111111111111111111111222222222222222222222222222222 \end{array} \right) \\ B_2= & {} \left( \begin{array}{c} 222222222222222222222222222222333333333333333333333333333333\\ 000001111122222333334444455555000001111122222333334444455555\\ 013450234501234123450124501235012350124512345023450123401345\\ 542313012401354540122315040235421050524305132103245134034251\\ 333333333333333333333333333333444444444444444444444444444444 \end{array} \right) \\ B_3= & {} \left( \begin{array}{c} 444444444444444444444444444444555555555555555555555555555555\\ 000001111122222333334444455555000001111122222333334444455555\\ 123450134502345012450123501234023451234501235012340134501245\\ 345105023141023213450523412540254034135015024502133254103412\\ 555555555555555555555555555555000000000000000000000000000000 \end{array} \right) \end{aligned}$$

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Shi, C., Jiang, L. & Tao, A. Consecutive Detecting Arrays for Interaction Faults. Graphs and Combinatorics 36, 1203–1218 (2020). https://doi.org/10.1007/s00373-020-02176-7

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  • DOI: https://doi.org/10.1007/s00373-020-02176-7

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