Generate boundary Value analysis, robust and worst-case test case for the program to find the median of three numbers. Its input is a triple of positive integers (say x, y, and z) and the minimum value can be 100 and maximum can be 500.
Median of three numbers is the middle number when all three numbers are sorted.
Example –
10, 40, 20
In this case, the median is 20 (10, 20, 40).
1. Boundary Value Test Cases are –
for x, y, z : min value = 100 close to min = 101 nominal = 300 close to max = 499 max = 500
Test cases are,
4*3 + 1 = 13
| X | Y | Z | Median |
|---|---|---|---|
| 100 | 300 | 300 | 300 |
| 101 | 300 | 300 | 300 |
| 300 | 300 | 300 | 300 |
| 499 | 300 | 300 | 300 |
| 500 | 300 | 300 | 300 |
| 300 | 100 | 300 | 300 |
| 300 | 101 | 300 | 300 |
| 300 | 499 | 300 | 300 |
| 300 | 500 | 300 | 300 |
| 300 | 300 | 100 | 300 |
| 300 | 300 | 101 | 300 |
| 300 | 300 | 499 | 300 |
| 300 | 300 | 500 | 300 |
2. Robust Test Cases –
Here, we go outside the legitimate boundary, it is an extension of boundary value analysis.
for x, y, z : min value : 100 close to min : 101 nominal : 300 close to max : 499 max : 500 lesser than min value : 99 larger than max value : 501
Total test cases,
= 6*n+1 = 6*3+1 = 19
So there will be extra 6 cases apart from the above 13 cases –
| X | Y | Z |
|---|---|---|
| 99 | 300 | 300 |
| 501 | 300 | 300 |
| 300 | 99 | 300 |
| 300 | 501 | 300 |
| 300 | 300 | 99 |
| 300 | 300 | 501 |
3. Worst Test Cases –
If we reject “single” fault assumption theory of reliability, and consider cases where more than 1 variable has extreme values, then it is known as worst case analysis.
Total no. of test cases,
5^n = 5^3 = 125 cases
| X | Y | Z | Median |
|---|---|---|---|
| 100 | 100 | 100 | 100 |
| 101 | 100 | 100 | 100 |
| 300 | 100 | 100 | 100 |
| 499 | 100 | 100 | 100 |
| 500 | 100 | 100 | 100 |
| 100 | 101 | 100 | 100 |
| 101 | 101 | 100 | 101 |
| 300 | 101 | 100 | 101 |
| 499 | 101 | 100 | 101 |
| … | … | … | … |
Mathematically, the test cases will be a cross product of 3 sets –
{100, 101, 300, 499, 500}
x {100, 101, 300, 499, 500}
x {100, 101, 300, 499, 500}
Let set A,
= {100, 101, 300, 499, 500}
So, the set of worst cases will be represented by,
= A x A x A
