Information Technology Reference
In-Depth Information
3
3
Fig. 1.2
OA
(
9
,
,
2
)
002
011
020
101
110
122
200
212
221
When some factors have the same level, we may combine them and make the
notation simpler. For example, 2
3
is the same thing as 2
·
2
·
2; it means the OA has
3 factors, each of which has two possible values.
Figure
1.2
shows a small example of OA whose strength is 2. We can see that,
for any two columns in the array, we get an even distribution of all the pairwise
combinations of values. Specifically, in any 9
×
2 subarray, each pair of values
appears exactly once. So the array is an OA.
For more examples, visit the library of OAs maintained by Sloane:
Orthogonal arrays can be regarded as natural generalizations of orthogonal Latin
squares. We can build an OA from a set of mutually orthogonal Latin squares (See
When an OA is used as a test suite, each row in the array corresponds to a test
case, and each factor corresponds to a component or parameter of the SUT.
Beautiful as they are, OAs have someweaknesses when used as test suites. In 1987,
Tatsumietal.[
38
,
39
] proposed to relax the requirement of a combinatorial test suite.
They think that it is enough if each tuple appears at least once; it is not necessary
that each tuple appears the same number of times. In the early 1990s, Sherwood [
35
]
also found limitations of OAs when applied to software/system testing. For example,
sometimes the required OA does not exist. Even if the OA exists, its size is often
quite large. Thus, in software testing, we usually do not use OAs, except for some
small SUTs.
1.3.3 Covering Arrays
In the last 20 years, most people use covering arrays (CAs) [
36
]forCT.
Definition 1.4
A
CA
(
N
,
d
1
·
d
2
···
d
k
,
t
)
of
strength t
is an
N
×
k
array having the
following properties:
(1) There are exactly
d
i
symbols in each column
i
(1
≤
i
≤
k
).
(2) In every
N
t
subarray, each ordered combination of symbols from the
t
columns
appears at least once.
×
Search WWH ::
Custom Search