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Boundary value analysis, Robustness Tetsing , Equivalence Class Testing
& Decision Table Testing
There are two types of testing
1. Black box testing ( by giving inputs test the output according to the requirements)
2. White box testing ( testing source code )
Example:- Requirement for age drop down (1-100)
If you select the values between 1 -100 it should accept, else it should display error message.
But it is not possible to test all the values from 1 to 100(time consuming)
To overcome that, two types of black box testing methods are there to derive test cases
1. Boundary value analysis
2. Equivalence class testing
BOUNDARY VALUE ANALYSIS
Boundary value analysis is one of the black box testing methods to derive test cases and to make sure it works
for all the values with in the boundary. Boundary value Test Cases are subset of Robustness Test Cases.
1. Boundary value Test cases of single input
2. Boundary value Test cases of two input
3. Boundary value Test cases of three input(additional info)
4. Worst case Boundary Value Test Cases of two inputs
5. Worst case Boundary Value Test Cases of three inputs
1.Boundary value Test cases of single input :Min+
Avg
Max|------|----------------------|------------------------|------|
Min
Max
Boundary value test cases of single input
Here we are testing within the boundaries (only valid data according to the requirement)
We are not testing for invalid data (out of boundary).
Min ---------------------------------- Minimal
Min+ ---------------------------------- Just above Minimal
Nom ---------------------------------- Average
Max ---------------------------------- Just below Maximum
Max ---------------------------------- Maximum
Example :Requirement: Age: 1-100
Boundary Value Test Cases are (min, min+1, avg, max-1, max)
1
2
51
99 100
Requirement: ATM PIN: 0000-9999
Boundary Value Test Cases are (min min+1 avg
0000 0001
5000
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max-1 max)
9998
9999
2
2.Boundary Value Test Cases of two inputs (x1, x2) are :-
{< x1 nom,x2min>,< x1 nom,x2min+>,< x1 nom,x2nom>,< x1 nom,x2max->,< x1 nom,x2max>,
<x1min+,x2nom>,<x1min,x2nom>, <x1max,x2nom>,<x1max-,x2nom> }
No. of test cases are 4n+1 (n is no of inputs)
Give each set of inputs and check whether the output is according to the requirement or not, instead of testing all
sets, you have to test the above set of inputs to make sure that it will work for all the values within the range.
Example of two inputs: To test whether multiplication is working correctly or not (we need 2 inputs)
Requirement: - c= a* b
(1<=a<=100, 1<=b<=100)
Boundary value sets of a and b are
a= {1,2,50,99 ,100} b={1,2,50,99,100}
Based on the above sets, combinations of test cases (input sets by BVA) are
{< x1 nom,x2min>,< x1 nom,x2min+>,< x1 nom,x2nom>,< x1 nom,x2max->,< x1 nom,x2max>,
<x1min+,x2nom>,<x1min,x2nom>, <x1max,x2nom>,<x1max-,x2nom> }
{(50,1),(50,2),(50 ,50),(50,99),(50,100),(1,50),(2,50)(99,50)(100,50)}
Take first set of inputs and check whether it is according to the requirement or not
Give first set input values are 50 and 1
c=50*1
It displays some result that is called actual result, if you know the multiplication(requirement) you can expect
the result that is called expected result (if both accepted result and actual result are same you can say first test
case is pass else fail)
Like above you have to test all sets of inputs one by one, Second set is (50, 2) give inputs and compare actual
and expected and decide whether the test case is pass or fail. Same way third set (50, 50), fourth (50, 99)...
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Table format of multiplication test cases (BVA)
Inputs
A
50
50
50
………….
Expected
Result
50
100
2500
…………..
B
1
2
50
…………….
Actual
Result
50
100
2500
……….
Status
Pass/fail
Pass
Pass
Pass
………….
3.Boundary value Test cases of three inputs are :{< x1 nom,x2min>,< x1 nom,x2min+>,< x1 nom,x2nom>,< x1 nom,x2max->,< x1 nom,x2max>,
<x1min+,x2nom>,<x1min,x2nom>, <x1max,x2nom>,<x1max-,x2nom> }
Example:*
{x3min , x3 min+1, x3 nom, x3max-1, x3max} (Cartesian product)
Requirement: Example triangle problem: 1 ≤ x1 ≤ 100,
1 ≤ x2≤ 100,
1 ≤ x3≤ 100 are three sides of triangle.
{(50,1),(50,2),(50 ,50),(50,99),(50,100),(1,50),(2,50)(99,50)(100,50)} * {1, 2, 50, 99,100}
{(50,1,1)(50,2,1)(50,50,1),(50,99,1)(50,100,1)……………………………………..}
Give each set of inputs and compare actual and expected results
Table format of triangle test cases using BVA
Inputs
x1
x2
50
1
50
50
……
2
50
……
x3
1
1
1
……..
Expected
Result
Actual
Result
Status
Pass/fail
Isosceles
Not a triangle
Fail
Scalene
Isosceles
……….
Scalene
Not a triangle
………..
Pass
Fail
………
4.Worst-case Boundary value analysis Test cases for two inputs:If you are not satisfied with Boundary value Test cases, that means you can’t make sure that,
The related functionality is working according to the requirements after testing with the above Boundary value
limited sets, and then we can go for Worst Case Testing.
In case of two inputs, consider all sets produced by the below Cartesian product
{x1 min, x1 min+1, x1 nom, x1max-1, x1max} * {x2 min, x2 min+1, x2 nom, x2max-1, x2max}
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These test cases although more comprehensive in their coverage, constitute much more endeavour. To compare we can
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see that Boundary Value Analysis results in 4n + 1 test case where Worst-Case testing results in 5 test cases. As each
variable has to assume each of its variables for each permutation (the Cartesian product) we have 5 to the n test cases.
5.Worst-Case Boundary value Test cases of three inputs triangle problem:Three sides of the triangle are x1, x2, x3 lies between1-200 test cases are
{{ {x1min,x1min+,x1nom,x1max,x1 max-} *{x2min,x2min+,x2nom,x2max,x2 max-}}*
}
{x3min, x3min+, x3nom, x3max, x3 max-}
} * {x3 min, x3 min+1, x3 nom, x3max-1, x3 max}
Total no.of test cases are 5 n
(N is no.of inputs)
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ROBUSTNESS TESTING
Robustness testing is an extension of boundary value analysis, to derive test cases and to make sure it will work
for all the values (valid and invalid) with in and out of the boundaries.
1. Robustness Test cases of single input
2. Robustness Test cases of two input
3. Robustness Test cases of three input(additional info)
4. Worst case Robustness Test Cases of two inputs
5. Worst case Robustness Test Cases of three inputs
1.Robustness Testing of single input
MinMin+
Avg
MaxMax+
|------|------|----------------------|------------------------|------|------|
Min
Max
Robustness Test Cases of single input
{ x1 mn-,x1min,x1min+,x1avg,x1max-,x1max,x1max+ }
Example: Requirement of ATM withdraw min amount is 100 max is 10,000
Robustness Test Cases are (Min-1, min, min+1, avg, max-1, max max+1)
0
1
2
51
99 100 101
2.Robustness Test Cases of two inputs a<= x1<=b,c<= x2<=d:-
{< x1 nom,x2min->,< x1 nom,x2min>,< x1 nom,x2min+>,< x1 nom,x2nom>,< x1 nom,x2max->,
<x1nom,x2max>,<x1nom,x2max+>,<x1min,x2nom>,<x1min,x2nom>,<x1min+,x2nom><x1max+,x2nom>,
<x1max,x2nom>,<x1max-,x2nom> }
No.of test cases are 6n+1 (n is no of inputs)
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Give each set of inputs and check whether the output is according to the requirement or not, instead of testing all
the values you have to test the above set of inputs to make sure it will work for all the values with in and out of the
boundaries(valid and invalid).
Example for writing Robustness Test Case of two inputs
To test whether addition is working correctly or not (2 inputs)
c= a+ b (1<=a<=100, 1<=b<=100)
a= {0,1,2,50,99,100,101} b={0,1,2,50,99,100,101}
Based on the above sets, combinations of test cases (inputs) are
{(50,0)(50,1),(50,2),(50 ,50),(50,99),(50,101),(50,100),(1,50),(2,50)(99,50)(100,50)(101,50)(0,50)}
Take first set of inputs and check whether it is according to the requirement or not
Give first set input values are 50 and 0
c=50+0
It displays some result that is called actual result, if you know the addition you can expect the result that is
called expected result (if both accepted result and actual result are same you can say first test case is pass else
fail)
Like this you have to test all sets of inputs one by one, second set is (50, 1) give inputs and compare actual and
expected and decide whether that is pass or fail. Same way third set (50, 2), fourth (50, 50)...
Table format of addition test cases (Robustness Testing)
Inputs
A
50
50
50
50
………….
B
0
1
2
50
…………….
Expected
Result
50
51
52
100
…………..
Actual
result
50
51
52
100
……….
Status
Pass/fail
Pass
Pass
Pass
Pass
………….
3.Robustness Test Cases In case of three inputs (example triangle problem):{<x1nom,x2min>,<x1nom,x2min>,<x1nom,x2min+>,<x1nom,x2nom>,<x1nom,x2max,<x1nom,x2max+>,<x1min,x2nom>,<x1min,x2nom>,<x1min+,x2nom><x1max+,x2nom>,
<x1max,x2nom>,<x1max-,x2nom> } * {x3 min-,x3 min, x3 min+1, x3 nom, x3 max-1, x3 max,x3
max+}
Requirement:1 ≤ x1 ≤ 100,
1 ≤ x2≤ 100,
1 ≤ x3≤ 100 are three sides of triangle.
Test cases are:{(50,0),(50,1),(50,2),(50 ,50),(50,99),(50,100),(50,101)(0,50),(1,50),(2,50)(99,50)(100,50),(101,50)} *
{0, 1, 2, 50, 99,100,101}
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{(50,0,0)(50,1,0)(50,2,0)(50,50,0),(50,99,0)(50,100,0)……………………………………..}
Give each set of inputs and compare actual and expected result
Table format of triangle test case (robustness testing)
Inputs
X1
50
50
50
………….
X2
0
1
2
…………….
X3
0
0
0
………..
Expected
Result
Actual
result
Status
Pass/fail
Isosceles
Scalene
Scalene
Not a triangle
Scalene
Scalene
Fail
Pass
Pass
…………..
……….
………….
4.Worst–Case Robustness Test Cases of two inputs :{ x1 mn-,x1min,x1min+,x1avg,x1max-,x1max,x1max+} *
{ x2 mn-,x2min,x2min+,x2avg,x2max-,x2max,x2max+ }
These test cases although more comprehensive in their coverage, constitute much more endeavour. To compare we can
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see that Robustness Testing results in 6n + 1 test case where Worst-Case testing results in 7 test cases. As each
variable has to assume each of its variables for each permutation (the Cartesian product) we have 7 to the n test cases.
Total no. of Test Cases is 7n
5.Worst-case Robustness Test cases of (three inputs) triangle problem(x1, x2, x3 are the sides):-
{ {x1 mn-,x1min,x1min+,x1avg,x1max-,x1max,x1max+} *
{ x2 mn-,x2min,x2min+,x2avg,x2max-,x2max,x2max+ }
* {x1 mn-,x1min,x1min+,x1avg,x1max-,x1max,x1max+}
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* {x3 min-,x3 min, x3 min+1, x3 nom, x3 max-1, x3 max,x3 max+}
Below are the few worst-case Robust ness Test Cases of triangle problem (1<=x1, x2, x3<=200)
Conclusion:
The above Test cases are used in the case of single or multiple inputs and inputs should have upper and
lower boundaries)

Not possible to test all the values so we can use this Black Box Testing methods

BVA Test Cases are sub set of Robustness Test Cases, using BVA we are testing within the boundaries
(valid inputs), in Robustness Testing we are testing with and with out of the boundaries (valid and invalid).

Best method to follow is Robustness testing.
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Equivalence Class Testing

Use the mathematical concept of partitioning into equivalence classes to generate test cases for Functional
(Black-box) testing
 The key goals for equivalence class testing are similar to partitioning:
o completeness of test coverage
o lessen duplication of test coverage
Partitioning : 
Recall a partitioning of a set, A, is to divide the set A into ( a1, a2, - - - -, an ) subsets such that:
o a1 U a2 U - - - - U an = A
(completeness)
o for any i and j, ai ∩ aj = Ø
(no duplication)
Equivalence Classes :
Equivalence class testing is the partitioning of the (often times, but not always) input variable’s value set
into classes (subsets) using some equivalence relation.
There are four types of Equivalence Class Testing types
1. Weak Normal Equivalence Class Testing
2. Strong Normal Equivalence Class Testing
3. Weak Robust Equivalence Class Testing
4. Strong Robust Equivalence Class Testing
Equivalence Class Test Cases of single input: In Boundary Value and Robustness Testing we are selecting the inputs at the boundary points and one avg value.
For example age- 0-100 in we are considering only -1,0,1, 50, 99,100 and 101 , but it may not accept when you
enter the age not at the boundary like 30 , 40, 60, 70 etc., we are not testing these values in BVA or RT to
overcome that we can go for Equivalence Class Testing.

Consider a numerical input variable, i, whose values may range from -200 through +200. Then a possible
partitioning of testing input variable by 4 people may be:
o
-200 to -100| -101 to 0|1 to 100|101 to 200
Inputs are -150, -50, 90, and 150
Weak Normal Equivalence testing of two inputs: Assumes the ‘single fault’ or “independence of input variables.”
 E.g. If there are 2 input variables, these input variables are independent of each other.
 Partition the test cases of each input variable separately into different equivalent classes.
 Choose the test case from each of the equivalence classes for each input variable independently of the other
input variable
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Strong Normal Equivalence testing of two inputs:•
•
This is the same as the weak normal equivalence testing except for
“Multiple fault assumption”
or
“Dependence among the inputs”
All the combinations of equivalence classes of the variables must be included.
Weak Robust Equivalence testing of two inputs:•
•
Up to now we have only considered partitioning the valid input space.
“Weak robust” is similar to “weak normal” equivalence test except that the invalid input variables are now
considered.
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Strong Robust Equivalence testing of two inputs:•
•
Does not assume “single fault” - - - assumes dependency of input variables
“Strong robust” is similar to “strong normal” equivalence test except that the invalid input variables are
now considered.
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Equivalence Class Test Cases for the Triangle Problem
•
We may define the input test data by defining the equivalence class through “viewing” the 4 output
groups:
R1-input sides <a, b, c> do not form a triangle
R2-input sides <a, b ,c> form an isosceles triangle
R3-input sides <a, b, c> form a scalene triangle
R4-input sides <a, b, c> form an equilateral triangle
Weak Normal Test Cases of Triangle problem
Test Case
WN1
WN2
WN3
WN4
A
5
2
3
4
b
5
2
4
1
C
5
3
5
2
Expected Output
Equilateral
Isosceles
Scalene
Not a Triangle
Weak Robust Test Cases of Triangle problem
Test Case
WR1
WR2
WR3
WR4
WR5
WR6
A
-1
5
5
201
5
5
b
5
-1
5
5
201
5
C
5
5
-1
5
5
201
Expected Output
Value a is not in range
Value b is not in range
Value c is not in range
Value a is not in range
Value b is not in range
Value c is not in range
Strong Robust Test Cases of Triangle problem
Test Case
SR1
SR2
SR3
SR4
SR5
SR6
SR7
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A
-1
5
5
-1
5
-1
-1
b
5
-1
5
-1
-1
5
-1
C
5
5
-1
5
-1
-1
-1
Expected Output
Value a is not in range
Value b is not in range
Value c is not in range
Value a,b is not in range
Value b,c is not in range
Value c,a is not in range
Value c,a,b is not in range
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Decision Table Testing
Decision Table-Based Testing has been around since the early 1960’s; it is used to analyze complex logical
relationships between input data.
Definition:A Decision Table is the method used to build a complete set of test cases without using the internal structure of the
program. In order to create test cases we use a table that contain the input and output values of a program. Such a table
is split up into four sections as shown below in fig 2.1.





In fig 2.1 there are two lines which divide the table into four components. The solid vertical line separates
the Stub and Entry portions of the table, and the solid horizontal line is the boundary between the
Conditions and Actions.
These lines separate the table into four portions, Condition Stub, Action Stub, Condition Entries and
Action Entries.
A column in the entry portion of the table is known as a rule.
Values which are in the condition entry columns are known as inputs and values inside the action entry
portions are known as outputs.
Outputs are calculated depending on the inputs and specification of the program
SAMPLE DECISION TABLE
RULES
ACTION ENTRIES
CONDITIONS
ACTIONS
CONDITION
ENTRIES
2.2 Typical Structure of Decission Table

The above table is an example of a typical Decision Table. The inputs in this given table derive the outputs
depending on what conditions these inputs meet.

Notice the use of “-“in the table below, these are known as don’t care entries. Don’t care entries are normally
viewed as being false values which don’t require the value to define the output.
Figure 2.2 shows its values from the inputs as true(T) or false(F) values which are binary conditions, tables
which use binary conditions are known as limited entry decision tables. Tables which use multiple conditions
are known as extended entry decision tables

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Redundancy Decision Table:When using “don’t care” entries a level of care must be taken, using these entries can cause redundancy and
inconsistency within a decision table.
An example of a decision table with a redundant rule can be seen in figure 3.3. From the table you can see that there is
some conflict between rules 1-4 and rule 9, rules 1-4 use “don’t care” entries as an alternative to false, but rule 9
replaces those “don’t care” entries with “false” entries. So when condition 1 is met rules 1-4 or 9 may be applied,
luckily in this particular instance these rules have identical actions so there is only a simple correction to be made to
complete the following table(we can remove any one rule1-4 or 9).
Figure 3.3 an example of a Redundant Rule
Inconsistency Decision Table :If on the other hand the actions of the redundant rule differ from that of rules 1-4 then we have a problem. A
showing this can be seen in figure 3.4.
table
Figure 3.4 an example of Inconsistent Rules
From the above decision table, if condition 1 was to be true and conditions 2 and 3 were false then rules 1-4 and 9
could be applied. This would result in a problem because the actions of these rules are inconsistent so therefore the
result is nondeterministic and would cause the decision table to fail.
Decision Table for Triangle Problem
As explained above, there are two types of decision table, limited and extended entry tables. Below, in fig 3.1 is an
example of a limited entry decision table where the inputs are binary conditions.
Fig 3.1 Decision Table for the Triangle Problem
Rule Counts :Rule counts are used along with don’t care entries as a method to test for decision table completeness; we can count the
no. of test cases in a decision table using rule counts and compare it with a calculated value. Below is a table which
illustrates rule counts in a decision table.
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Fig 3.2 an example of Rule Counts in a Decision Table
The table above has a total rule count of 64; this can be calculated using the limited entry formula as it’s a limited entry
table. Number of Rules = 2n (n is no. of conditions)
So therefore, Number of Rules =26 = 64 When calculating rule counts the don’t care values play a major role to find the
rule count of that rule.
Test cases for the triangle problem based on 3.2 diagram
DT1
DT2
DT3
DT4
DT5
DT6
DT7
DT8
DT9
DT10
DT11
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A
B
C
Expected Output
4
1
1
5
2
2
3
3
1
4
2
5
2
3
2
4
2
2
4
5
3
2
2
5
Not a Triangle
Not a Triangle
Not a Triangle
Equilateral
Impossible
Impossible
Isosceles
Impossible
Isosceles
Isosceles
Scalene