Improve: Solutions & DOE

A full factorial design investigates 3 factors, each at 2 levels, with no replication. How many experimental runs are required?

• A 6
• B 8 ✓
• C 9
• D 16

Answer: A two-level full factorial requires 2^k runs; with k = 3 factors this is 2^3 = 8 runs.

In a designed experiment, an 'interaction' between two factors means that:

• A The two factors are statistically correlated before the experiment
• B The effect of one factor on the response depends on the level of the other factor ✓
• C Both factors must be set to their high level to improve the response
• D The factors can be analysed only one at a time

Answer: An interaction exists when the effect of one factor on the response changes depending on the setting of another factor, something one-factor-at-a-time testing cannot detect.

Why is randomization of run order important in a designed experiment?

• A It reduces the total number of runs needed
• B It helps prevent unknown lurking variables (such as time-related trends) from biasing the results ✓
• C It forces the response to follow a normal distribution
• D It guarantees that all interactions are estimable

Answer: Randomizing run order spreads the influence of uncontrolled, time-dependent factors across the design so they do not systematically bias the estimated effects.

The primary purpose of a fractional factorial design is to:

• A Eliminate the need for randomization
• B Estimate every possible interaction with maximum precision
• C Screen many factors with far fewer runs than a full factorial ✓
• D Replicate the centre point many times

Answer: Fractional factorial designs use a carefully chosen subset of runs to screen many factors economically, accepting that some higher-order effects become confounded.

In a fractional factorial design, 'confounding' (aliasing) means that:

• A The factors were set at the wrong levels
• B The response data are non-normal
• C Two or more effects cannot be estimated separately because they are linked by the design ✓
• D The experiment contains too many replicates

Answer: Confounding (aliasing) occurs when the design cannot distinguish certain effects from one another, so their estimates are combined and cannot be separated.

A poka-yoke is best described as a technique that:

• A Ranks improvement ideas against weighted criteria
• B Charts process output over time
• C Measures process capability against specifications
• D Mistake-proofs a process so errors are prevented or made obvious ✓

Answer: Poka-yoke (mistake-proofing) designs the process so that errors are prevented from occurring or are immediately detected, reducing reliance on inspection.