1. Chapter 2: Boundary Value Testing : BVT 322235 Software TestingBy
Dr. Wararat Songpan (Rungworawut)
Faculty of Computer Science,
Department of Science,
Khon Kaen University, Thailand

2. Guideline of Boundary Value Testing
This technique focuses on variable as number.

3. Boundary Value Testing : BVT
BVT is a black box testing technique
There are 4 sub-techniques of BVT
1) Boundary Value Analysis: BVA
2) Robustness Testing: RT
3) Worst-Case Testing: WT
4) Robust Worst-Case Testing: RWT

4. 1) Boundary Value Analysis: BVA
When the function F is implemented as a program, the input variable x1 and x2 will have boundaries as follows,
a =< x1 =< b
c =< x2 =< d x2 d c x1 a b

5. Example: A function of addition
Spec.
1<=x1<=10
Function: Addition X1 and x2 x1 x2
Spec.
1<=x2<=10
Results =

6. 1) Boundary Value Analysis: BVA(Cont.)
The 5 values used to test the extremities are:
1) minimum (min)
2) above minimum (min+)
3) nominal (nom)
4) below maximum (max-)
5) maximum (max)

7. 1) Boundary Value Analysis: BVA(Cont.)
BVA Test cases for function F X1 X2
Expected Results
x1nom
x2min
x2min+
x2nom
x2max-
x2max
x1min
x1min+
x1max-
x1max
The number of test case is 4n+1
,where n is the number of variable

8. 1) Boundary Value Analysis: BVA(Cont.)
BVA Test cases for function F of addition X1 X2
Expected Results 5 1 6 2 7 10 9 14 15 ?
Function: Addition X1 and x2 x1 x2
Results =

9. 1) Boundary Value Analysis: BVA(Cont.)
The idea and motivation behind BVA is that errors tend to occur near the extremities of the input variables. The defects found on the boundaries of these input variables can obviously be the result of countless possibilities.
For example if the programmer forgot to count from zero or they just miscalculated. Errors in the code concerning loop counters being off by one or the use of a < operator instead of ≤.
One of the values taking on their extreme values at any one particular time. The reason for this is that generally Boundary Value Analysis uses that called “Single Fault Assumption”.

10. Example: The Triangle Problem
Problem statements (Simple version)
input 3 integers: a, b, c are side of triangle
Output is type of triangle
Equilateral
Isosceles
Scalene
Not a Triangle (how to chek it?)

11. Example: The Triangle Problem
Problem statements (Improved version)
input 3 integers: a, b, c are side of triangle
Spec and condition
c1: 1 =< a =< c4: b+c > a (As a triangle)
c2: 1 =< b =< c5: a+c > b (As a triangle)
c3: I =< c =< c6: a+b > c (As a triangle)
Output is type of triangle
Equilateral
Isosceles
Scalene
Not a Triangle

12. The Triangle Problem: Flowchart
Input a, b, c
Match=0 y
a=b?
Match=Match+1 n
a=c? y
Match=Match+2 n
b=c? y
Match=Match+3 n
Match=0? y
a+b ≤ c? n n n
Match=1? y y
a+b ≤ c?
b+c ≤ a?
Match=2? y y y n n
a+c ≤ b? n y
a+c ≤ b?
Match=3? n y y n n
b+c ≤ a? y
Equilateral
Not a Triangle
Scalene n
Isosceles

13. Triangle: BVA Test Cases Design
Test case ID a b c
Expected Results
Actual Results 1
100
Isosceles 2 3
Equilateral 4
199 5
200
Not a Triangle 6 7 8 9 10 11 12 13 14 15

14. Example: The Next Date Function
Problem Statements
input 3 variables: month, date, year
Output:
as the next date from input the date
Spec. and Conditions:
C1: January =< month =< December
C2: 1 =< day =< 31
C3: 1812 =< year =< 2012
**Remark: The year should be verified as leap year

15. Leap Year
One year has the length of 365 days, 5 hours, 48 minutes and 47 seconds.
A normal year has been given 365 days and a leap year 366 days.
So at leap years February 29th is added, which doesn't exist in a normal year.
A leap year is every 4 years, but not every 100 years, then again every 400 years.
For example:
1992 is Leap Year (1992 mod 4 = 0 but1992 mod 100 and 400 ≠ 0)
1900 is NOT a Leap Year (1900 mod 4 and 1900 mod100 = 0 but 1900 mod 400 ≠ 0)
2000 is Leap Year (2000 mod 4,100 and 400 = 0)

16. Next Date: BVA Test Cases Design
Test case ID
Month
Day
Year
Expected Results
Actual Results 1
June 15
1812
June 16, 1812 2
1813
June 16, 1813 3
1912
June 16, 1912 4
2011
June 16, 2011 5
2012
June 16, 2012 6 7 8 9 30 10 31 11
January 12
February 13 14
November
December

17. 2) Robustness Testing: RT
Robustness testing can be seen as and extension of Boundary Value Analysis.
The idea behind Robustness testing is to test input variables that fall just outside this input domain.
We use two more values for each variable min- and max+ which are designed to fall just outside of the input range.
Robustness testing is still “Single Fault Assumption” because one of the values taking on their 7 extreme values at any one particular time.

18. 2) Robustness Testing: RT
Robustness Test cases for function F X1 X2
Expected Results
x1nom
x2min-
Alert message (out of range)
x2min
x2min+
x2nom
x2max-
x2max
x2max+
x1min-
x1min
x1min+
x1max-
x1max
x1max+
The number of test case is 6n+1
,where n is the number of variable

19. 3) Worst-Case Testing: WT
Worst-case Testing uses the critical fault assumption for more than one variable at a time assuming its extreme values called “multiple faults assumption”
So we are able to test the outcome if more than one variable were to assume its extreme value.
To generate test cases we take the original 5 extreme values (min, min+, nom, max-, max) and perform the Cartesian product of these values. The end product is a much larger set of results than we have seen before.

20. 3) Worst-Case Testing: WT(Cont.)
Worst-Case Test cases for function F x1 x2
min
min+
nom
max-
max
min
min+
nom
max-
max
The number of test case is 5n
,where n is the number of variable

21. 3) Worst-Case Testing: WT(Cont.)
Worst-Case Test cases for function F X1 X2
Expected Results
x1min
x2min
x2min+
x2nom
x2max-
x2max
x1min+ …
Software Testing

22. 4) Robust Worst-Case Test: RWT
If the function under test were to be of the greatest importance we could use a method named Robust Worst-Case testing which as the name suggests draws it attributes from Robust Worst-Case testing.
Test cases are constructed by taking the Cartesian product of the 7 extreme values (min-, min, min+, nom, max-, max, max+)
There are more than one variable at a time assuming its extreme values occurred critical fault called “multiple faults assumption”

23. 4) Robust Worst-Case Test: RWTx2 x1
min-
min
min+
nom
max-
max
max+
min-
min
min+
nom
max-
max
max+
The number of test case is 7n
,where n is the number of variable

24. 4) Robust Worst-Case Test: RWT
Robust Worst-Case Test cases for function F X1 X2
Expected Results
x1min-
x2min-
x2min
x2min+
x2nom
x2max-
x2max
x2max+
x1min …
Software Testing

25. How to use Boundary Value Testing (BVT)
BVT is considered in 2 approaches:
1) By the number of variables.
We could use a certain set integer, we could allow the program to use the highest or lowest possible integer.
2) By the kind of ranges.
For example in the Next Date example
Some languages to declare an enumerated type {Jan, Feb, Mar,......, Dec}. It would normally encode for testing of the month’s variable so that January corresponded to 1 and February corresponded to 2 etc.

26. Summary of Boundary Value Testing (BVT)
BVT only focuses on variable as number.
BVT works well for consideration the function of several independent variables that represent boundary value such as Triangle Program. But it is not good enough for the next date program that has dependent variable.

27. Summary of Boundary Value Testing (BVT)
BVT has divided into 2 characteristics:
1) Normal vs Robust value
Normal (Valid)
Robust (Valid+Invalid)
Boundary Value Analysis
Worst-Case Testing
Robustness Testing
Robust Worst-Case Testing
2) Single fault vs multiple fault assumption
Single fault (1 and extreme value)
Multiple fault (1+ and extreme value)
Boundary Value Analysis
Robustness Testing
Worst-Case Testing
Robust Worst-Case Testing