Objectives.

Expanding upon the concept of Orthogonal Arrays are Covering Arrays.

This Tutorial will give a quick introduction to what covering arrays are.

Goals:

1. Understand what Covering Arrays are

2. Learn how Covering Arrays can be expanded into Sequence Covering Arrays.

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Not every combination of variables and values has a corresponding Orthogonal array. In addition because there is no single unified method to generate Orthogonal Arrays they are not always easy to construct

Worst of all Orthogonal arrays can be larger then necessary because of their requirement that each pair of inputs occur the same number of times.

By relaxing that rule you can create Covering Arrays. Covering arrays are easier to construct and can be smaller then Orthogonal Arrays while still testing as much.

Let's start with a basic example.

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OA(8,7,2,2)

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CA(6,7,2)

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Here the first two variables are highlighted. Notice how the pairs (0,1) and (1,0) occur twice in the Orthogonal Array but only occur once in the Covering Array.

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One of the largest benifits of Covering Arrays comes when dealing with constraints. As constraints are added onto a problem it becomes increasing difficult to map the problem to something as strict as an Orthogonal Array.

Covering arrays, on the other hand, can be adjusted much easier.

Take a look at the tutorial on constraints in combinatorics here to get a better idea of what they are and how they works.

Let's see how else Covering Arrays can be used to generate tests.

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There are times when when some components are especially interconnected. Because of this it might be a good idea to focus additional testing on these components.

For these situations use a Variable Strength Covering Array.

Denoted by VCA(N; t, k, s(C)) where C represents a vector of covering arrays each of strength > t defined on a subset of the k columns.

A simple example will illustrate this concept.

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A Camera configuration

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A CA(5,2,4,2)

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A CA(5,2,4,2)

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A VCA(8,2,4,2(CA(N,3,3,2))

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A VCA(8,2,4,2(CA(N,3,3,2))

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Recap.

Covering arrays work extremely well in software testing and are much easier to create then Orthogonal Arrays.

This often makes them the best choice for Combinatorial Interaction Testing.

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