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# Software testing method for boundary value analysis using orthogonal array

IP.com Disclosure Number: IPCOM000012770D
Publication Date: 2003-May-28
Document File: 3 page(s) / 95K

## Publishing Venue

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## Abstract

ID890463

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ID 890463

Software testing method for boundary value analysis using orthogonal array

Description

Maximum number of errors in software tends to occur at the boundaries of the input domain than in the “center”. It is for this reason that boundary value analysis (BVA) has been developed as a testing technique. Boundary value analysis leads to a selection of test cases that exercise bounding values.

The Orthogonal Array has a mathematical foundation in linear algebra—specifically, the Galois field theory—began with Euler as Latin squares.

Definition of Latin square

A (n × n) Latin square is a square array with n rows and n columns in which n letters are placed in such a way that

·         there is 1 letter in each cell (row-column intersection)

·         each letter occurs once in each row and once in each column.

Latin square is an orthogonal array of degree n, strength 1. For example, Latin Square of degree 3 is:

 1 2 3 2 3 1 3 1 2

Genichi Taguchi [1] and Phadke[2], have provided a convenient tabulation of Orthogonal Arrays and associated linear graphs to facilitate construction of arrays for specific needs. Orthogonal array is a two-dimensional array of numbers, which has interesting quality that by choosing any two columns in the array you receive all the pair-wise combinations of values in the array.

For example, Orthogonal array of degree 3, levels 2 and strength 2 (see Phadke[2]):

 1 1 1 1 2 2 2 1 2 2 2 1

• There are three columns;
• Any two columns of the array, you will see each ordered pair of symbols precisely once

For example, Orthogonal array of degree 4, levels 2 and strength 2 (see Phadke[2]):

 1 1 1 1 1 2 2 2 1 3 3 3 2 1 2 3 2 2 3 1 2 3 1 2 3 1 3 2 3 2 1 3 3 3 2 1

There are four columns i.e. four parameters of software. Any two columns of the array (Example column 1 and 3), you will see each ordered pair of symbols precisely once {(1,1), (1,2) …. (3,2)}. Each parameter is having three levels. Let, level 1 is for normal value of parameter, level 2 is for minimum value of parameter and level 3 is for maximum value of the parameter. Test cases for four parameters using proposed method and BVA are shown in Table-1.

Table.1: Test Plan using Proposed Method and BVA

Proposed Method (OA)   BVA
Test Case   Test Parameters   Test Case   Test Parameters
A   B   C   D   A   B   C   D
1   1   1   1   1   1   1   1   1   1
2   1   2   2   2   2   2   1   1   1
3   1   3   3   3   3   3   1   1   1
4   2   1   2   3   4   1   2   1   1
5   2   2   3   1   5   1   3   1   1
6   2   3   1   2   6   1   1   2   1
7   3   1   3   2   7   1   1   3   1
8   3   2   1   3   8   1   1   1   2
9   3   3   2   1   9   1   1   1   3

Fig. 1: OA and BVA Test Cases. To facilitate geometric visualization, take the above example of software with only three test parameters A, B, and C. The test domain is cube-shaped and consists of 27 lattice points. Test cases based on the proposed (see Table-1) and based on the BVA method are graphically displayed in Fig.1. Whereas the BVA test cases cover only a small region of the test domain, the proposed cases are dispersed uniformly throughout the test domain. Thus, the proposed test cases greatly increase t...