Modified Condition or Decision Coverage

software-engineering testing

Definition

MC/DC

Modified Condition/Decision Coverage (MC/DC) is a rigorous structural testing metric that extends Decision Coverage. It requires that each atomic condition in a decision be shown to independently affect the decision’s outcome.

Requirements:

1. Every atomic condition has taken all possible outcomes (True/False).
2. Every decision (branch) has taken all possible outcomes (True/False).
3. Each condition is shown to independently determine the result (changing only that condition changes the decision output).

All or Nothing

Unlike other metrics (e.g., “80% Statement Coverage”), MC/DC is typically considered binary. It is either fully achieved or not; partial coverage is rarely used as a metric.

Concept

MC/DC serves as a practical compromise between the insufficient testing of simple condition/branch coverage and the exponential complexity of testing all $2^n$ combinations of conditions.

• Efficiency: It requires $n+1$ test cases for a decision with $n$ conditions (linear complexity) instead of $2^n$ (exponential).
• Usage: It is mandated for safety-critical systems (e.g., avionics software).

Independence Pair

To prove that condition c independently affects the decision, we need a pair of test cases ($T_1,T_2$) such that:

1. Condition c is True in $T_1$ and False in $T_2$.
2. All other conditions remain constant (have the same truth values in both tests).
3. The outcome of the decision in $T_1$ is different from $T_2$.

Example

Consider the decision if (A && (B || C)).

Truth Table Analysis:

ID	A	B	C	Result
1	T	T	T	T
2	T	T	F	T
3	T	F	T	T
4	T	F	F	F
5	F	T	T	F
6	F	T	F	F
7	F	F	T	F
8	F	F	F	F

Independence Pairs:

1. For A:
   • Needs $A$ to toggle ($T\leftrightarrow F$), others fixed, result toggles.
   • Pairs: $\{1,5\},\{2,6\},\{3,7\}$.
   • (Note: $\{4,8\}$ is invalid because Result $F\leftrightarrow F$ does not change).
2. For B:
   • Needs $B$ to toggle ($T\leftrightarrow F$), others fixed, result toggles.
   • Pairs: $\{2,4\}$.
3. For C:
   • Needs $C$ to toggle ($T\leftrightarrow F$), others fixed, result toggles.
   • Pairs: $\{3,4\}$.

Minimal Test Suite: To satisfy MC/DC, we select a subset of tests that cover at least one independence pair for every condition.

• Selected Set: $\{2,3,4,6\}$
  • A is covered by pair $(2,6)$.
  • B is covered by pair $(2,4)$.
  • C is covered by pair $(3,4)$.
• Efficiency: We achieved full coverage with 4 tests ($n+1$) instead of the full 8 ($2^n$).