Selecting the Best Wild Card Entries in a Covering Array

Abstract

For some covering arrays, there are some wild card positions in the array where there is flexibility about what factor levels can be chosen with no impact on the basic properties of covering array, because all of the required pairs have been covered. The choice of how to fill these wild card positions can influence other properties, such as the degrees of orthogonality or three-way coverage of the array. In this paper, some criteria are proposed for identifying the best choices for the wild card positions to create covering arrays with highly desirable properties. Accompanying graphical summaries are also described to highlight differing performance for several examples.

Methods to Construct Uniform Covering Arrays

“…The postoptimization method of Nayeri et al [99] is based on detecting wildcards to select the rows to be eliminated. The method of Kim et al [102] replaces wildcards in a CA of strength two by other valid symbols; this is done with the objective of finding CAs of strength two that have high desirable properties, such as a good coverage of 3-tuples. ; 2, v + 1, v) to produce an MCA(v…”