Because systems testing is expensive, reducing the amount of testing is critical. Testing all possible interactions is usually prohibitive and often unnecessary. Experience shows that most failures result from the interaction of a small number of components. The size of the largest combination of components likely to drive a failure, called the strength, drives the size of the design.
For background on the structure of covering arrays and algorithms for computing them, see Colbourn (2004), Colbourn et al. (2011), Hartman and Raskin (2004), and Martirosyan (2003). For details about covering arrays with restrictions on factor levels, see Cohen et al. (2007) and Morgan (2009).
A covering array of strength t is a design that tests all combinations of t factor level settings. Consider an interaction defined by specific settings for k factors. If failures occur for all tests involving that interaction, then that interaction detects a failure. Using this terminology, a strength t design enables you to detect failures associated with any interaction of up to t factors.
In the literature, covering arrays are also referred to as factor covering designs. For background and details, see Yilmaz et al. (2014), Cohen et al. (2003), and Dalal and Mallows (1998).
Figure 19.2 A Resolution III Design with Strength 2
Note that this design is a strength 2 covering array because all pairwise combinations of levels of any two factors appear. For example, for X1 and X2, the following combinations each appear twice:
However, the 6-run design in Figure 19.3 is also a strength 2 covering array:
Figure 19.3 Strength 2 Covering Array