Mathematics in quality assurance

MATHEMATIQA*Equivalence classes partitioning

*Boundary Value Analysis(abridged version)

Alexandr Szpinkowski, PhD

Plan

• Philosophical aspect

• Mathematical foundations

• Examples

Philosophical aspect

Category (from the Greek, kategoria - statement, accusation, sign) is extremely general term that expresses the most significant relationship to reality. The study of the categories is in determining the most fundamental and wide entity classes.

Philosophical aspect

Categories (according to Kant)

Emmanuel Kant, the great German philosopher (1724-1804)

Categories Quantity: •Unity •Plurality •Totality

CategoriesQuality:•Reality•Negation•Limitation

CategoriesRelation:

■Inherence and Subsistence (substance and accident)

■Causality and Dependence (cause and effect)

■Community (reciprocity)

Mathematical foundations

Set theory is the branch of mathematics that studies sets, which are collections of objects

Splitting the set into pairwise disjoint subsets called classification, and the resulting subsets are called classes.

Equivalence relationa given binary relation ~ on a set X is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive.

Reflexive Property: (a=a)a is equivalent to a example: 2 = 2; 5+4 = 5+4

Symmetric Property: (if a=b, then b=a)a = b is equivalent to b =aexample: 5+4 = 4+5

Transitive Property: (if a=b and b=c, then a=c)example:.5 = 1/2; 1/2 = 2/4 therefore .5 = 2/4

Equivalence Partitioning also called as equivalence class partitioning. It is abbreviated as ECP. It is a software testing technique that divides the input test data of the application under test into each partition at least once of equivalent data from which test cases can be derived.

An advantage of this approach is it reduces the time required for performing testing of a software due to less number of test cases.

Example

Assume that the application accepts an integer in the range 100 to 999 Valid Equivalence Class partition: 100 to 999 inclusive. Non-valid Equivalence Class partitions: less than 100, more than 999, decimal numbers and alphabets/non-numeric characters.

Boundary value analysis focuses on values on the edge of an equivalence partition or at the smallest value on either side of an edge.

Example:Test cases for input box accepting numbers between 1 and 1000 using Boundary value analysis:

• Test cases with test data exactly as the input boundaries of input domain i.e. values 1 and 1000 in our case.

• Test data with values just below the extreme edges of input domains i.e. values 0 and 999.

• Test data with values just above the extreme edges of input domain i.e. values 2 and 1001.

References:• http://en.wikipedia.

org/wiki/Equivalence_partitioning • http://en.wikipedia.

org/wiki/Boundary_value_analysis • http://www.softwaretestinghelp.com/what-

is-boundary-value-analysis-and-equivalence-partitioning/

• http://www.scribd.com/doc/49845951/6/Equivalence-Partitioning

• www.software-testng.ru• http://trancecyberiantester.blogspot.

com/2013/09/DevsVsTest.html • http://www.solving-math-problems.

com/math-properties-reflexive-symmetric-transitive.html

Thank You

e-mail: alexandr.szpinkowski@gmail.com