### Abstract

Covering arrays with mixed alphabet sizes, or mixed covering arrays, are useful generalizations of covering arrays that are motivated by software and network testing. Suppose that there are k factors, and that the ith factor takes values or levels from a set G_{i} of size g_{i}. A run is an assignment of an admissible level to each factor. A mixed covering array, MCA(N;t,k,g_{1}g_{2}...g_{k}), is a collection of N runs such that for any t distinct factors, i_{1},i_{2},...,i_{t}, every t-tuple from G_{i1}×G_{i2}×. .×G_{it} occurs in factors i_{1},i_{2},...,i_{t} in at least one of the N runs. When g=g_{1}=g_{2}=...=g_{k}, an MCA(N;t,k,g_{1}g_{2}...g_{k}) is a CA(N;t,k,g). The mixed covering array number, denoted by MCAN(t,k,g1g2...gk), is the minimum N for which an MCA(N;t,k,g_{1}g_{2}...g_{k}) exists. In this paper, we focus on the constructions of mixed covering arrays of strength three. The numbers MCAN(3,k,g_{1}g_{2}...g_{k}) are determined for all cases with k∈{3,4} and for most cases with k∈;{5,6}.

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

Pages (from-to) | 3640-3647 |

Number of pages | 8 |

Journal | Journal of Statistical Planning and Inference |

Volume | 141 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2011 |

### Fingerprint

### Keywords

- Covering array
- Mixed covering array
- Orthogonal array

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

### Cite this

*Journal of Statistical Planning and Inference*,

*141*(11), 3640-3647. https://doi.org/10.1016/j.jspi.2011.05.018

**Mixed covering arrays of strength three with few factors.** / Colbourn, Charles; Shi, Ce; Wang, Chengmin; Yan, Jie.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 141, no. 11, pp. 3640-3647. https://doi.org/10.1016/j.jspi.2011.05.018

}

TY - JOUR

T1 - Mixed covering arrays of strength three with few factors

AU - Colbourn, Charles

AU - Shi, Ce

AU - Wang, Chengmin

AU - Yan, Jie

PY - 2011/11

Y1 - 2011/11

N2 - Covering arrays with mixed alphabet sizes, or mixed covering arrays, are useful generalizations of covering arrays that are motivated by software and network testing. Suppose that there are k factors, and that the ith factor takes values or levels from a set Gi of size gi. A run is an assignment of an admissible level to each factor. A mixed covering array, MCA(N;t,k,g1g2...gk), is a collection of N runs such that for any t distinct factors, i1,i2,...,it, every t-tuple from Gi1×Gi2×. .×Git occurs in factors i1,i2,...,it in at least one of the N runs. When g=g1=g2=...=gk, an MCA(N;t,k,g1g2...gk) is a CA(N;t,k,g). The mixed covering array number, denoted by MCAN(t,k,g1g2...gk), is the minimum N for which an MCA(N;t,k,g1g2...gk) exists. In this paper, we focus on the constructions of mixed covering arrays of strength three. The numbers MCAN(3,k,g1g2...gk) are determined for all cases with k∈{3,4} and for most cases with k∈;{5,6}.

AB - Covering arrays with mixed alphabet sizes, or mixed covering arrays, are useful generalizations of covering arrays that are motivated by software and network testing. Suppose that there are k factors, and that the ith factor takes values or levels from a set Gi of size gi. A run is an assignment of an admissible level to each factor. A mixed covering array, MCA(N;t,k,g1g2...gk), is a collection of N runs such that for any t distinct factors, i1,i2,...,it, every t-tuple from Gi1×Gi2×. .×Git occurs in factors i1,i2,...,it in at least one of the N runs. When g=g1=g2=...=gk, an MCA(N;t,k,g1g2...gk) is a CA(N;t,k,g). The mixed covering array number, denoted by MCAN(t,k,g1g2...gk), is the minimum N for which an MCA(N;t,k,g1g2...gk) exists. In this paper, we focus on the constructions of mixed covering arrays of strength three. The numbers MCAN(3,k,g1g2...gk) are determined for all cases with k∈{3,4} and for most cases with k∈;{5,6}.

KW - Covering array

KW - Mixed covering array

KW - Orthogonal array

UR - http://www.scopus.com/inward/record.url?scp=79959780043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959780043&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2011.05.018

DO - 10.1016/j.jspi.2011.05.018

M3 - Article

AN - SCOPUS:79959780043

VL - 141

SP - 3640

EP - 3647

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 11

ER -