### Abstract

When k factors each taking one of v levels may affect the correctness or performance of a complex system, a test is selected by setting each factor to one of its levels and determining whether the system functions as expected (passes the test) or not (fails). In our setting, each test failure can be attributed to at least one faulty (factor, level) pair. A nonadaptive test suite is a selection of such tests to be executed in parallel. One goal is to minimize the number of tests in a test suite from which we can determine which (factor, level) pairs are faulty, if any. In this paper, we determine the number of tests needed to locate faults when exactly one (or at most one) pair is faulty. To do this, we address an equivalent problem, to determine how many set partitions of a set of size N exist in which each partition contains v classes and no two classes in the partitions are equal.

Original language | English (US) |
---|---|

Pages (from-to) | 2011-2026 |

Number of pages | 16 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 30 |

Issue number | 4 |

DOIs | |

State | Published - 2016 |

### Fingerprint

### Keywords

- Baranyai's theorem
- Covering array
- Locating array
- Sperner partition system

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*SIAM Journal on Discrete Mathematics*,

*30*(4), 2011-2026. https://doi.org/10.1137/16M1056390

**Disjoint spread systems and fault location.** / Colbourn, Charles; Fan, Bingli; Horsley, Daniel.

Research output: Contribution to journal › Article

*SIAM Journal on Discrete Mathematics*, vol. 30, no. 4, pp. 2011-2026. https://doi.org/10.1137/16M1056390

}

TY - JOUR

T1 - Disjoint spread systems and fault location

AU - Colbourn, Charles

AU - Fan, Bingli

AU - Horsley, Daniel

PY - 2016

Y1 - 2016

N2 - When k factors each taking one of v levels may affect the correctness or performance of a complex system, a test is selected by setting each factor to one of its levels and determining whether the system functions as expected (passes the test) or not (fails). In our setting, each test failure can be attributed to at least one faulty (factor, level) pair. A nonadaptive test suite is a selection of such tests to be executed in parallel. One goal is to minimize the number of tests in a test suite from which we can determine which (factor, level) pairs are faulty, if any. In this paper, we determine the number of tests needed to locate faults when exactly one (or at most one) pair is faulty. To do this, we address an equivalent problem, to determine how many set partitions of a set of size N exist in which each partition contains v classes and no two classes in the partitions are equal.

AB - When k factors each taking one of v levels may affect the correctness or performance of a complex system, a test is selected by setting each factor to one of its levels and determining whether the system functions as expected (passes the test) or not (fails). In our setting, each test failure can be attributed to at least one faulty (factor, level) pair. A nonadaptive test suite is a selection of such tests to be executed in parallel. One goal is to minimize the number of tests in a test suite from which we can determine which (factor, level) pairs are faulty, if any. In this paper, we determine the number of tests needed to locate faults when exactly one (or at most one) pair is faulty. To do this, we address an equivalent problem, to determine how many set partitions of a set of size N exist in which each partition contains v classes and no two classes in the partitions are equal.

KW - Baranyai's theorem

KW - Covering array

KW - Locating array

KW - Sperner partition system

UR - http://www.scopus.com/inward/record.url?scp=85006999715&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006999715&partnerID=8YFLogxK

U2 - 10.1137/16M1056390

DO - 10.1137/16M1056390

M3 - Article

AN - SCOPUS:85006999715

VL - 30

SP - 2011

EP - 2026

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 4

ER -