Information Technology Reference
In-Depth Information
Fig. 1.5 Some values of
CAN (for t = 2)
k N
3 4
4 5
10 6
15 7
35 8
56 9
126 10
210 11
d
k N
4 9
5 11
7 12
9 13
10 14
20 15
21 16
28 17
d
k N
10 76
11 78
13 84
15 96
16 102
18 104
19 107
20 108
d
k N
13 153
14 155
15 158
16 161
17 171
18 177
19 178
20 186
d
=
2
=
3
=
8
=
11
When a CA is used as a test suite, each row of the array represents a test case,
and the i th column corresponds to the values of parameter p i in the test cases.
Sometimes, testing using a CA of strength t is called t -way or t -wise testing. When
the strength is 2, the testing is also called pairwise testing . In such a test suite, for
any two components/parameters of the SUT, every pair of values appears in at least
one test case.
In the literature, people use CAN
(
d 1 ·
d 2 ···
d k ,
t
)
to denote the smallest number N
for which CA
exists. It is called the covering array number . When
all the d i 's are equal to v , we denote the number by CAN
(
N
,
d 1 ·
d 2 ···
d k ,
t
)
(
v
,
k
,
t
)
or CAN
(
t
,
k
,
v
)
.
Thus, CAN
.
Some specific CANs are available at a website maintained by Charlie Colbourn:
http://www.public.asu.edu/~ccolbou/src/tabby/catable.html
Just to give the readers an impression of the sizes of test suites, we list some known
bounds 1 in Fig. 1.5 .
(
t
,
k
,
v
) =
min
{
N
|∃
CA
(
N
;
t
,
k
,
v
) }
1.4 Covering Arrays for Testing
When applying CAs to software testing, we often feel it necessary to extend the concept
in various ways.
1.4.1 Seeding
Sometimes, there are some important parameter combinations that must be tested, such
as the default configurations of newly-deployed software. Seeding first introduced by
[ 8 ] allows testers to explicitly specify some parameter combinations (called seeds )tobe
1 Obtained from Colbourn's website, April 26, 2014. Note that the values given here are just the
current best known results. It is possible that we will find smaller values in the future, for some
cases.
 
 
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