1462:'Enabled', 'Choice Type' and 'Category' have a choice range of 2, 3 and 4, respectively. An exhaustive test would involve 24 tests (2 x 3 x 4). Multiplying the two largest values (3 and 4) indicates that a pair-wise tests would involve 12 tests. The pairwise test cases, generated by Microsoft's "pict" tool, are shown below.
63:
In most cases, a single input parameter or an interaction between two parameters is what causes a program's bugs. Bugs involving interactions between three or more parameters are both progressively less common and also progressively more expensive to find, such testing has as its limit the testing
64:
of all possible inputs. Thus, a combinatorial technique for picking test cases like all-pairs testing is a useful cost-benefit compromise that enables a significant reduction in the number of test cases without drastically compromising functional coverage.
1103:
1771:
IEEE 12. Proceedings from the 5th
International Conference on Software Testing and Validation (ICST). Software Competence Center Hagenberg. "Test Design: Lessons Learned and Practical Implications
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are the number of possibilities for each of the two parameters with the most choices, and it can be quite a lot less than the exhaustive
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where comma denotes any combination. If the code is written as conditions taking "pairs" of parameters, then the set of choices of ranges
306:. Imagining that the code deals with the conditions taking only two parameters at a time, might reduce the number of needed test cases.
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Kuhn, D. Richard; Kacker, Raghu N.; Yu Lei (October 2010). Practical
Combinatorial Testing. SP 800-142 (Report).
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of order 3, which takes all 3 as input, or rather three different order 2 predicates of the form
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The N-wise testing then would just be, all possible combinations from the above formula.
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47:), tests all possible discrete combinations of those parameters. Using carefully chosen
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Pragmatic
Software Testing: Becoming an Effective and Efficient Test Professional
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1970:
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Pairwise
Testing in the Real World: Practical Extensions to Test-Case Scenarios
1098:{\displaystyle P_{s}=<P_{i}>\;;\;i<j\implies |R(P_{i})|<|R(P_{j})|}
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29:
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N-wise testing can be considered the generalized form of pair-wise testing.
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and call it the pairwise testing. Generalizing further we can take the set
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1996:
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Kuhn, D. Richard; Wallace, Dolores R.; Gallo, Albert M. Jr. (June 2004).
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637:
The number of pair-wise test cases on this test function would be:-
1845:
1705:"Software Fault Interactions and Implications for Software Testing"
577:
55:
of all parameters by "parallelizing" the tests of parameter pairs.
41:
879:
309:
To demonstrate, suppose there are X,Y,Z parameters. We can use a
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51:, this can be done much faster than an exhaustive search of
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276:. We note that the number of all possible test cases is a
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and call it the 3-wise testing. Eventually, we can say
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Pairwise
Testing - Combinatorial Test Case Generation
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Pairwise and generalized t-way combinatorial testing
1369:{\displaystyle X(T)=\{P_{N-1},P_{N-2},...,P_{N-T}\}}
530:{\displaystyle p_{xy}(X,Y),p_{yz}(Y,Z),p_{zx}(Z,X)}
170:{\displaystyle \{P_{i}\}=\{P_{1},P_{2},...,P_{N}\}}
67:More rigorously, if we assume that a test case has
1387:Consider the parameters shown in the table below.
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1265:{\displaystyle X(3)=\{P_{N-1},P_{N-2},P_{N-3}\}}
1747:National Institute of Standards and Technology
40:of input parameters to a system (typically, a
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960:gets ordered too. Let the sorted set be a
177:. The range of the parameters are given by
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1712:IEEE Transactions on Software Engineering
1173:{\displaystyle X(2)=\{P_{N-1},P_{N-2}\}}
825:then the number of tests is typically O(
818:{\displaystyle m=max(X\setminus max(X))}
430:can be written in an equivalent form of
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1642:
617:is one of the maximum of the multiset
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13:
1645:"Efficient Testing with All-Pairs"
14:
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1773:. July 18, 2008. pp. 1–150.
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2118:Graphical user interface testing
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219:{\displaystyle R(P_{i})=R_{i}}
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269:{\displaystyle |R_{i}|=n_{i}}
2143:Software reliability testing
2082:Software performance testing
1779:10.1109/IEEESTD.2008.4578383
58:
7:
1612:
953:{\displaystyle P=\{P_{i}\}}
914:{\displaystyle X=\{n_{i}\}}
860:{\displaystyle \prod n_{i}}
569:{\displaystyle X=\{n_{i}\}}
299:{\displaystyle \prod n_{i}}
10:
2200:
1985:Testing types, techniques,
1382:
87:parameters given in a set
2110:
1984:
1953:
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2128:Orthogonal array testing
2077:Smoke testing (software)
2047:Dynamic program analysis
1629:
1624:Orthogonal array testing
1107:Now we can take the set
756:{\displaystyle n=max(X)}
423:{\displaystyle P(X,Y,Z)}
347:{\displaystyle P(X,Y,Z)}
1756:10.6028/NIST.SP.800-142
1643:Berger, Bernie (2003).
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610:{\displaystyle max(S)}
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2184:Design of experiments
2007:Compatibility testing
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878:The idea is to apply
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2042:Differential testing
1653:TechWell Corporation
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226:. Let's assume that
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2037:Development testing
2032:Destructive testing
2022:Conformance testing
1966:Integration testing
1911:Model-based testing
1901:Exploratory testing
1724:10.1109/TSE.2004.24
1674:Black, Rex (2007).
2092:Symbolic execution
2067:Regression testing
2027:Continuous testing
2017:Concurrent testing
1961:Acceptance testing
1884:The "box" approach
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722:Therefore, if the
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2102:Usability testing
1928:White-box testing
1896:All-pairs testing
1891:Black-box testing
1788:978-0-7381-5746-7
1689:978-0-470-12790-2
1610:
1609:
1460:
1459:
973:{\displaystyle N}
630:{\displaystyle S}
80:{\displaystyle N}
22:all-pairs testing
2191:
2174:Software testing
2072:Security testing
2057:Negative testing
2012:Concolic testing
1938:Mutation testing
1923:Grey-box testing
1916:Scenario testing
1877:Software testing
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1376:T-wise testing.
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53:all combinations
34:software testing
26:pairwise testing
18:computer science
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2097:Test automation
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1682:. p. 240.
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2148:Stress testing
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2123:Manual testing
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1820:External links
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1718:(6): 418–421.
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871:N-wise testing
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30:combinatorial
27:
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19:
2138:Soak testing
2133:Pair testing
1976:Unit testing
1906:Fuzz testing
1895:
1770:
1765:
1740:
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1711:
1698:
1678:. New York:
1675:
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1657:. Retrieved
1651:
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882:to the set
877:
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313:of the form
308:
66:
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49:test vectors
37:
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2153:Web testing
1997:A/B testing
1933:API testing
1659:21 November
1471:Choice type
1427:Choice type
2168:Categories
36:that, for
32:method of
2002:Benchmark
1807:ignored (
1797:cite book
1732:206778290
1474:Category
1356:−
1325:−
1306:−
1252:−
1233:−
1214:−
1160:−
1141:−
1031:⟹
845:∏
829:), where
792:∖
687:∖
669:×
576:can be a
311:predicate
284:∏
59:Rationale
45:algorithm
38:each pair
2111:See also
1613:See also
1444:Category
1405:Value 4
921:so that
578:multiset
42:software
1989:tactics
1468:Enabled
1410:Enabled
1402:Value 3
1399:Value 2
1396:Value 1
1383:Example
880:sorting
1785:
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1728:S2CID
1708:(PDF)
1680:Wiley
1648:(PDF)
1630:Notes
1589:False
1556:False
1545:False
1534:False
1512:False
1501:False
1416:False
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