The correct answer is B. 2ⁿ⁻¹ . In DOE, a full factorial experiment for n factors at two levels requires 2ⁿ runs . A half-fraction design uses exactly one-half of those runs, so the number of runs becomes:

(1/2)(2ⁿ) = 2ⁿ⁻¹

The CSSBB material identifies these as two-level fractional factorial designs and explains that fractional designs are used to reduce the number of experimental trials while still learning about the most important factor effects. This is a standard Six Sigma Improve-phase concept because DOE is often used to optimize a process efficiently without running every possible treatment combination.

The other options represent different design sizes. 2ⁿ is the full factorial. 2ⁿ⁻² would be a quarter-fraction, and 2ⁿ⁻³ would be an eighth-fraction. Therefore, when the question specifically asks for a half-fraction run for a two-level design with n factors , the correct mathematical expression is 2ⁿ⁻¹ . That makes option B the verified answer.