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• W2000832753 abstract "A k × n array with entries from an “alphabet” A = { 0 , 1 , … , q − 1 } of size q is said to form a t -covering array (resp. orthogonal array) if each t × n submatrix of the array contains, among its columns, at least one (resp. exactly one) occurrence of each t -letter word from A (we must thus have n = q t for an orthogonal array to exist and n ≥ q t for a t -covering array). In this paper, we continue the agenda laid down in Godbole et al. (2009) in which the notion of consecutive covering arrays was defined and motivated; a detailed study of these arrays for the special case q = 2 , has also carried out by the same authors. In the present article we use first a Markov chain embedding method to exhibit, for general values of q , the probability distribution function of the random variable W = W k , n , t defined as the number of sets of t consecutive rows for which the submatrix in question is missing at least one word. We then use the Chen–Stein method ( Arratia et al., 1989 , Arratia et al., 1990 ) to provide upper bounds on the total variation error incurred while approximating L ( W ) by a Poisson distribution Po ( λ ) with the same mean as W . Last but not least, the Poisson approximation is used as the basis of a new statistical test to detect run-based discrepancies in an array of q -ary data." @default.
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• W2000832753 date "2010-05-01" @default.
• W2000832753 modified "2023-09-24" @default.
• W2000832753 title "Consecutive covering arrays and a new randomness test" @default.
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• W2000832753 doi "https://doi.org/10.1016/j.jspi.2009.11.016" @default.
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