Masking MC/DC? What's all that about then?

2012-10-13

If you're involved in developing and verifying high integrity software (especially if DO-178B is involved), you have probably come across the use of MC/DC (modified condition/decision coverage) for helping to demonstrate that tests are thorough enough.

Sometimes, the use of masking MC/DC is also discussed. In this blog post, I briefly describe how masking MC/DC is different from "regular" (unique cause) MC/DC.

Before I talk about what masking MC/DC is, let's briefly recap what MC/DC is. In a complex decision (for example, the expression within an if-statement), you have to run enough tests to demonstrate that each individual condition can independently affect the outcome. (We also discuss this in more detail in a previous blog post). This means that for an if statement:

If (A and B) or (C and D) then
    X;
else
    Y;

You need to run pairs of tests where:

B, C, D remain constant. By varying A you get two different outcomes (X or Y)
A, C, D remain constant. By varying B you get two different outcomes
A, B, D remain constant. By varying C you get two different outcomes
A, B, C remain constant. By varying D you get two different outcomes

Each of these pairs of tests is termed an independence pair.

This suggests that we need four pairs of tests. However, if you’re smart about it, you can combine one member of an independence pair with another member of an independence pair. If you manage to do this at the best level possible, the testing can be done with five tests (in general N+1 tests for N conditions).

This relies on all of the conditions being independent. This approach is termed unique-cause MC/DC.

So what happens if conditions aren’t independent? This is where masking MC/DC comes in. Masking refers to the approach where specific conditions can mask the effects of other conditions.

The masking approach to MC/DC allows more than one condition to change in an independence pair, as long as the condition of interest is shown to be the only condition that affects the value of the decision outcome.

Using the above example, to show that A can independently affect the outcome of the decision, test cases require that B is true and (C and D) is false, so:

If A is true, the outcome is true
If A is false, the outcome is false

Provided that in both test cases (i.e where A is false and where A is true), the subexpression (C and D) is false, masking MC/DC allows the values of C and D to vary, so for example the following test vectors would be acceptable: