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# Robustness Analysis – Quadratic Equation Problem

• Last Updated : 24 Jan, 2023

Robustness Testing is the extended version of Boundary value analysis. It is a Black Box software testing technique. It does not examine the internal structure or design of the system.

Boundaries are a very good place for errors to occur. If we design software and generate test cases, the value within a specified range has less probability for errors to occur. The values just below and above the boundary or at the boundary have a higher chance to generate an error.

Assuming the interval [x, y]

1. Values between x and y: Less chance to generate error.
2. x – 1, x, x + 1, y – 1, y, y + 1: More chance to generate error.

### Single Fault Assumption

When we check more than one variable for the same software then single fault assumption can be used. Holding all but one variable to extreme values one by one.

Total Number of Test Cases for ‘n’ variables: (6n+1) test cases.

In designing the test cases for robustness testing, we have to determine the total number of input variables. For each input variable, we determine the extreme values and nominal values.

Example: Consider a program for the determination of the nature of the roots of a Quadratic Equation. Its input is triple of a positive integer and the values range from 0 to 100.

Expected Outputs:

Not a quadratic equation: a = 0

Real roots: (b2 − 4ac) > 0

Imaginary roots: (b2−4ac) < 0

Equal roots: (b2−4ac) = 0

Solution:

The range according to the problem statement:

0 ≤ a ≤ 100
0 ≤ b ≤ 100
0 ≤ c ≤ 100

The nominal value can be taken as = (0 + 100) / 2
= 50.

Total number of test cases = 6 * n + 1
= 6 * 3 + 1
= 19 test cases

The table below shows the test case design for the quadratic equation problem. The range is taken as [0, 100] and the nominal value is taken as 50.

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