Chapter 2: Boundary Value Testing : BVT
322235 Software Testing
By
Asst.Prof.Dr. Wararat Songpan (Rungworawut)
Department of Computer Science,
Faculty of Science,
Khon Kaen University, Thailand
Guideline of Boundary Value Testing
• This technique focuses on variable as number.
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
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,
x2
d
c
x1
a
b
• a =< x1 =< b
• c =< x2 =< d
Example: A function of addition
Function: Addition X1 and x2
x1
Spec.
1<=x1<=10
x2
Results =
Spec.
1<=x2<=10
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)
1) Boundary Value Analysis: BVA(Cont.)
 BVA Test cases for
function F
The number of test case is 4n+1
,where n is the number of variable
X1
X2
x1nom
x2min
x1nom
x2min+
x1nom
x2nom
x1nom
x2max-
x1nom
x2max
x1min
x2nom
x1min+
x2nom
x1nom
x2nom
x1max-
x2nom
x1max
x2nom
Expected
Results
1) Boundary Value Analysis: BVA(Cont.)
 BVA Test cases for
function F of addition
X1
X2
Expected
Results
5
1
6
5
2
7
5
5
10
5
9
14
5
10
15
?
?
?
Function: Addition X1 and x2
x1
x2
Results =
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”.
Example: The Triangle Problem
• Problem statements (Simple version)
• input 3 integers: a, b, c are side of triangle
• Output is type of triangle
o Equilateral
o Isosceles
o Scalene
o Not a Triangle (how to chek it?)
Example: The Triangle Problem
• Problem statements (Improved version)
o input 3 integers: a, b, c are side of triangle
• Spec and condition
o c1: 1 =< a =<200
o c2: 1 =< b =<200
o c3: I =< c =< 200
• Output is type of triangle
o
o
o
o
Equilateral
Isosceles
Scalene
Not a Triangle
c4: b+c > a (As a triangle)
c5: a+c > b (As a triangle)
c6: a+b > c (As a triangle)
The Triangle Problem: Flowchart
Input a, b, c
Match=0
y
a=b?
Match=Match+1
n
y
a=c?
Match=Match+2
n
y
b=c?
Match=Match+3
n
n
Match=1
?
Match=2
?
n
Equilateral
a+b ≤ c?
n
y
y
a+b ≤ c?
y
n
Match=3
?
y
Match=0
?
n
b+c ≤ a?
y
y
a+c ≤ b?
y
y
b+c ≤ a?
n
n
n
n
y
y
Isosceles
Not a Triangle
a+c ≤ b?
n
Scalene
Triangle: BVA Test Cases Design
Test case
ID
a
b
c
Expected Results
1
100
100
1
Isosceles
2
100
100
2
Isosceles
3
100
100
100
Equilateral
4
100
100
199
Isosceles
5
100
100
200
Not a Triangle
6
100
1
100
Isosceles
7
100
2
100
Isosceles
8
100
100
100
Equilateral
9
100
199
100
Isosceles
10
100
200
100
Not a Triangle
11
1
100
100
Isosceles
12
2
100
100
Isosceles
13
100
100
100
Equilateral
14
199
100
100
Isosceles
15
200
100
100
Not a Triangle
Actual Results
Example: The Next Date Function
• Problem Statements
o input 3 variables: month, date, year
• Output:
o as the next date from input the date
• Spec. and Conditions:
o C1: January =< month =< December
o C2: 1 =< day =< 31
o C3: 1812 =< year =< 2012
**Remark: The year should be verified as leap year
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:
o 1992 is Leap Year (1992 mod 4 = 0 but1992 mod 100 and 400 ≠ 0)
o 1900 is NOT a Leap Year (1900 mod 4 and 1900 mod100 = 0 but 1900 mod
400 ≠ 0)
o 2000 is Leap Year (2000 mod 4,100 and 400 = 0)
Next Date: BVA Test Cases Design
Test case
ID
Month
Day
Year
Expected Results
1
June
15
1812
June 16, 1812
2
June
15
1813
June 16, 1813
3
June
15
1912
June 16, 1912
4
June
15
2011
June 16, 2011
5
June
15
2012
June 16, 2012
6
June
1
1912
7
June
2
1912
8
June
15
1912
9
June
30
1912
10
June
31
1912
11
January
15
1912
12
February
15
1912
13
June
15
1912
14
November
15
1912
15
December
15
1912
Actual Results
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.
2) Robustness Testing: RT
 Robustness Test cases for function F
The number of test case is 6n+1
,where n is the number of variable
X1
X2
Expected Results
x1nom
x2min-
Alert message (out of
range)
x1nom
x2min
x1nom
x2min+
x1nom
x2nom
x1nom
x2max-
x1nom
x2max
x1nom
x2max+
x1min-
x2nom
x1min
x2nom
x1min+
x2nom
x1nom
x2nom
x1max-
x2nom
x1max
x2nom
x1max+
x2nom
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.
3) Worst-Case Testing: WT(Cont.)
 Worst-Case Test cases for function F
The number of test case is 5n
,where n is the number of variable
x1
x2
min
min+
nom
maxmax
min
min+
nom
maxmax
3) Worst-Case Testing: WT(Cont.)
 Worst-Case Test cases for function F
322 235 Software Testing
X1
X2
x1min
x2min
x1min
x2min+
x1min
x2nom
x1min
x2max-
x1min
x2max
x1min+
x2min
x1min+
x2min+
x1min+
x2nom
x1min+
x2max-
x1min+
x2max
…
…
…
…
Expected Results
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”
4) Robust Worst-Case Test: RWT
x1
The number of test case is 7n
,where n is the number of variable
minmin
min+
nom
maxmax
max+
x2
minmin
min+
nom
maxmax
max+
4) Robust Worst-Case Test: RWT
 Robust Worst-Case Test cases for function F
322 235 Software Testing
X1
X2
x1min-
x2min-
x1min-
x2min
x1min-
x2min+
x1min-
x2nom
x1min-
x2max-
x1min-
x2max
x1min-
x2max+
x1min
x2min-
x1min
x2min
x1min
x2min+
…
…
…
…
Expected Results
How to use Boundary Value Testing
(BVT)
• BVT is considered in 2 approaches:
1) By the number of variables.
o 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.
o For example in the Next Date example
o 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.
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.
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