1. Chapter 3: Equivalence Class Testing :EC 322235 Software TestingBy
Asst.Prof.Dr. Wararat Songpan (Rungworawut)
Department of Computer Science,
Faculty of Science,
Khon Kaen University, Thailand

2. Equivalence Class Testing : EC
The next step from Boundary Value Testing is a Functional Testing.
Define equivalence classes on the range of input or output for each variables also called partition method.
Completeness and greatly reduces redundancy.

3. Equivalence Class Testing : EC
Function F is implemented and a function F, of two variables x1 and x2.
x1 and x2 have the following boundaries and intervals within boundaries:
a=<x1=<d with intervals [a,b), [b,c), [c,d]
e=<x2=<g with intervals [e,f), [f,g]
So, invalid value for x1 and x2 as follows,
x1 < a and x1>d
x2 <e and x2>g
Remarks: [ = closed interval, ( = open interval

4. Equivalence Class Testing : EC
There are 4 sub-techniques of Equivalence Class Testing.
1) Weak Normal Testing :WN
2) Strong Normal Testing :SN
3) Weak Robust Testing :WR
4) Strong Robust Testing :SR

5. 1) Weak Normal Testing :WN
Valid EC:
Ec1 = {x1: a=<x1< b}
Ec2= {x1: b=<x1< c}
Ec3 = {x1: c <= x1 <= d}
Ec4 = {x2: e =<x2 < f}
Ec5 = {x2: f =< x2 <=g} x2 g f e x1 a b c d
One variable from each equivalence class as “single fault assumption”
Values identified in systematic way

6. For example: Addition x1 and x2 (Simple example)
Function: Addition X1 and x2 x1 x2
Results = Ok
Cancel

7. Simple example: WN Test case design
Valid EC:
Ec1 = {x1: 5=<x1< 10}
Ec2= {x1: 10=<x1< 15}
Ec3 = {x1: 15 <= x1 <= 20}
Ec4 = {x2: 5 =<x2 <10}
Ec5 = {x2: 10=< x2 <=20} 20 10 5 x1 5 10 15 20
Test case ID
EC ID x1 x2
Expected Results
WN1
EC1, EC4 5 6 11
WN2
EC2, EC5 12 15 27
WN3
EC3, EC4 17 7 24

8. 2) Strong Normal Testing : SNx2 g f e x1 a b c d
Test cases taken from each element of Cartesian product of the equivalence classes. Cartesian product guarantees notion of completeness.
SN is a “multiple fault assumption”

9. Simple example: SN Test case design
Valid EC:
Ec1 = {x1: 5=<x1< 10}
Ec2= {x1: 10=<x1< 15}
Ec3 = {x1: 15 <= x1 <= 20}
Ec4 = {x2: 5 =<x2 <10}
Ec5 = {x2: 10=< x2 <=20} 20 10 5 x1 5 10 15 20
Test case ID
EC ID x1 x2
Expected Results
SN1
EC1, EC4 5 6 11
SN2
EC1, EC5 7 12 19
SN3
EC2, EC4 10 15
SN4
EC2, EC5 27
SN5
EC3, EC4 17 24
SN6
EC3, EC5 30

10. 3) Weak Robust Testing (WR)x2
Additional consider in Invalid EC:
Ec6 = {x1: x1 < a}
Ec7 = {x1: x1 > d}
Ec8 = {x2 : x2 < e}
Ec9 = {x2 : x2 > g} g f e x1 a b c d
Robust - consideration of invalid values and extension to WN.
Invalid inputs – each test case has one invalid value, single fault should cause failure as “single fault assumption”.
Problems with robust EC Testing specification (expected output for invalid TC?)

11. Simple example: WR Test case design
Test case ID
EC ID x1 x2
Expected Results
WR1
EC1, EC4 5 6 11
WR2
EC2, EC5 12 15 27
WR3
EC3, EC4 17 7 24
WR4
EC6, EC4 4 8
X1 is out of range
WR5
EC7, EC4 23
WR6
EC3, EC8 18
X2 is out of range
WR7
EC3, EC9

12. 4) Strong Robust Testing :SRx2 g f e x1 a b c d
Robust - consideration of invalid values and extension to SN.
Strong – multiple faults assumption.
Test cases taken from each element of Cartesian product of the Valid EC and Invalid EC

13. Triangle Program (Simple)
Input 3 integers: a, b, c are side of triangle that have boundaries
a, b, c are [1,200].
Output is type of triangle
Equilateral
Isosceles
Scalene
Not a Triangle

14. WN Test case design Triangle Program (Simple)
Valid EC
EC1: 1<=a<= 200
EC2: 1<=b<=200
EC3: 1<=c<=200
Test Case
EC ID a b c
Expected Results
WN1
EC1,2,3 10 20 30
Scalene

15. SN Test case design Triangle Program (Simple)
Valid EC
EC1: 1<=a< 200
EC2: 1<=b<=200
EC3: 1<=c<=200
Test Case EC a b c
Expected Results
SN1
EC1,2,3 10 20 30
Scalene

16. Equivalence Class : Triangle Problem (Output)
Using output from specification translate into Equivalence Class (EC)
4 possible outputs: Equilateral, Isosceles, Scalene, and Not a Triangle
4 output equivalence classes:
Ec1 = {<a,b,c> : the triangle with sides a, b and c is equilateral}
Ec2 = {<a,b,c> : the triangle with sides a, b and c is Isosceles}
Ec3 = {<a,b,c> : the triangle with sides a, b and c is Scalene) }
Ec4 = {<a,b,c> : the triangle with sides a, b and c is Not a Triangle}

17. Weak Normal(WN)/ Strong Normal(SN) Test Cases: Triangle Program
Test Case ID EC a b c
Expected Results
OWN1
EC1 5
Equilateral
OWN2
EC2 2 3
Isosceles
OWN3
EC3 4
Scalene
OWN4
EC4 1
Not a Triangle

18. Weak Robust(WR) Test Cases: Triangle Program
Consideration Invalid EC with WN
EC5: a> 200
EC6: a < 1
EC7: b>200
EC8: b < 1
EC9: c>200
EC10: c<1

19. Weak Robust(WR) Test Cases: Triangle Program
Test Case ID EC a b c
Expected Results
WN1
…WN4
WR1
EC6 -1 5
a not in range
WR2
EC8
b not in range
WR3
EC10
c not in range
WR4
EC5
201
WR5
EC7
WR6
EC9

20. Strong Robust(SR) Test Cases: Triangle Program
Expected Results
WN1
…WN4
SR1 -1 5
a not in range
SR2
b not in range
SR3
c not in range
SR4
a, b not in range
SR5
b, c not in range
SR6
a, c not in range
SR7
a, b, c not in range

21. Improved EC: Triangle Program
Improved EC Input classes for each type of triangle:
EC1 = {<a, b, c>: a=b=c}
EC2 = {<a, b, c>: a=b, a ≠ c}
EC3 = {<a, b, c>: a=c, a ≠ b}
EC4 = {<a, b, c>: b=c, a ≠ b}
EC5 = {<a, b, c>: a ≠ b, a ≠ c, b ≠ c }
Extra design of input classes: Check every side of triangle as not a triangle
EC6 = {<a, b, c>: b + c <= a}
EC7 = {<a, b, c>: a + c <= b}
EC8 = {<a, b, c>: a + b <= c}

22. Equivalence Classes(EC) : NextDate Problem
Valid EC
M1 = {month: 1 =< month =<12}
D1 = {day: 1 =< day =< 31}
Y1 = {year: 1812 =< year =< 2012}
Invalid EC
M2 = {month: month <1}
M3 = {month: month >12}
D2 = {day: day <1}
D3 = {day: day >31}
Y2 = {year: year < 1812}
Y3 = {year: year > 2012}

23. Weak Normal and Strong Normal Test Cases: NextDate Problem
Month
Day
Year
Expected Results
WN1, SN1 6 15
1912
6/16/1912

24. Weak Robust Test Cases: The NextDate Problem
Test Case ID
Month
Day
Year
Expected Results
WN1 6 15
1912
6/16/1912
WR1 -1
Month not in range 1…12
WR2 13
WR3
Day not in range 1…31
WR4 32
WR5
1811
Year not in range 1812…2012
WR6
2013

25. Strong Robust Test Cases: The NextDate Problem
Month
Day
Year
Expected Results
WN1 6 15
1912
6/16/1912
SR1 -1
month not in range 1…12
SR2
day not in range 1…31
SR3
1811
year not in range 1812…2012
SR4
SR5
SR6
SR7

26. Improved Input Equivalence Classes: NextDate Problem
M1 = {month: month has 30 days}
M2 = {month: month has 31 days}
M3 = {month: month = February}
D1 = {day: 1 =< day =< 28}
D2 = {day: day = 29}
D3 = {day: day = 30}
D4 = {day: day = 31}
Y1 = {year: year is leap year}
Y2 = {year: year is common year }

27. Input Equivalence Class: The Commission Problem
Valid EC
L1 = {lock: 1 =< locks =< 70}
S1 = {stocks: 1=< stocks =< 80}
B1 = {barrels: 1 =< barrels =< 90}
Invalid EC
L2 = {locks: locks <1}
L3 = {locks: locks > 70}
S2 = {stocks: stocks < 1}
S3 = {stocks: stocks > 80}
B2 = {barrels: barrels <1}
B3 = {barrels: barrels >90}

28. Strong Robust Test Cases: Commission Problem
Test Case ID
Locks
Stocks
Barrels
Expected Results
SR1 5 50
SR2 -1 40 45
Locks not in range 1…70
SR3 35
Stocks not in range 1…80
SR4
Barrels not in range 1…90
SR5
SR6
SR7
SR8

29. Using output to Equivalence Classes Test Cases: Commission Problem
Sales = 45 * locks +30 * stocks + 25 * barrels
S1 = {<locks, stocks, barrels>: sales =<1000}
S2 = {<locks, stocks, barrels>: 1000 < sales =<1800}
S3 = {<locks, stocks, barrels>: sales > 1800 }
How to design WN Test Case??
Test Case ID
Locks
Stocks
Barrels
Sales
Commission
(Expected Results)
OWN1 5
500 50
OWN2 15
1500
175
OWN3 25
2500
360

30. Specification of Commission
Sales = 45*Locks + 30*Stock + 25*barrels
if sales <= 1000
commission = 10% * sales
if sales > 1000
commission = 10%* %*(sales – 1000)
if sales > 1800
commission = 10%* %* %* (sales-1800)

31. Summary of EC Testing Normal vs Robust
Normal (Valid)
Robust (Valid +Invalid)
Weak Normal Testing
Strong Normal Testing
Weak Robust Testing
Strong Robust Testing
Single fault vs Multiple fault assumption
Single fault (1 EC)
Multiple fault (1 EC+)
Weak Normal Testing
Weak Robust Testing
Strong Normal Testing
Strong Robust Testing