Summary: A \(k\times n\) array with entries from an “alphabet” \(\mathcal A = \{0,1,\dots,q-1\}\) of size \(q\) is said to form a \(t\)-covering array (resp. orthogonal array) if each \(t\times n\) submatrix of the array contains, among its columns, at least one (resp. exactly one) occurrence of each \(t\)-letter word from \(\mathcal A\) (we must thus have \(n=qt\) for an orthogonal array to exist and \(n\geq q^t\) for a \(t\)-covering array). In this paper, we continue the agenda laid down in [A. P. Godbole et al., “Binary consecutive covering arrays”, to appear in Ann. Inst. Statist. Math.] 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 [R. Arratia et al., Ann. Probab. 17, No. 1, 9–25 (1989; Zbl 0675.60017); Stat. Sci. 5, No. 4, 403–434 (1990; Zbl 0955.62542)] to provide upper bounds on the total variation error incurred while approximating \(\mathcal L(W)\) by a Poisson distribution \(Po(\lambda )\) 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.