Lean Six Sigma Black Belt Improve Phase: DOE Questions and Answers

Question 1

A Six Sigma team is planning a Design of Experiments (DOE) to understand a complex process with 7 factors. The team has limited time and resources, so a full factorial experiment is not feasible. They need to identify the most influential factors (main effects) for further investigation. Which type of experimental design is most appropriate for this initial stage?

Accepted Answer

A screening design, such as a fractional factorial

Answer

Screening experiments, like fractional factorial designs, are specifically used to efficiently identify the 'vital few' factors from the 'trivial many' when dealing with a large number of potential variables. [17, 22] They require significantly fewer runs than a full factorial design, making them ideal for situations with resource constraints. [5, 7] RSM is used for optimization later, a full factorial is too large, and OFAT is inefficient.

Question 2

In a fractional factorial Design of Experiments, the term 'resolution' is used to describe the degree of confounding. What is the primary characteristic of a Resolution III design?

Accepted Answer

Main effects are confounded with two-factor interactions.

Answer

A Resolution III design is one where main effects are aliased (confounded) with two-factor interactions. [12, 25, 29] This is the lowest practical resolution, as Resolution II would confound main effects with each other. Resolution IV designs separate main effects from two-factor interactions, and Resolution V designs separate both main effects and two-factor interactions from each other. [12, 30]

Question 3

A Black Belt is setting up a DOE and decides to include several runs where all factors are set at their midpoint level. What is the primary purpose of adding these 'center points' to the experiment?

Accepted Answer

To check for curvature in the relationship between factors and the response.

Answer

The primary reason for adding center points to a two-level factorial design is to detect curvature. [1, 3] If the response at the center point is significantly different from the average of the factorial points, it indicates a non-linear relationship. Center points also provide an estimate of pure error and can increase the statistical power of the design. [3, 8]

Question 4

During the execution of a designed experiment, an unexpected machine calibration issue occurred halfway through the runs. To account for this known source of variation, which is not one of the primary factors being studied, the experimenter should use which technique?

Accepted Answer

Blocking

Answer

Blocking is the technique used to account for known, controllable nuisance factors that could affect the response. [6, 10] By grouping the experimental runs into blocks (e.g., before and after calibration), the variability from the nuisance factor can be isolated and removed from the experimental error, leading to a more accurate analysis of the primary factors. [2, 13]

Question 5

Which of the following is a primary advantage of using a full factorial DOE compared to a fractional factorial DOE?

Accepted Answer

It allows for the estimation of all main effects and all interaction effects, free from confounding.

Answer

The key strength of a full factorial design is that it tests every possible combination of factor levels. [5, 11] This allows for the independent estimation of all main effects and all interactions between the factors, with no confounding. Fractional factorials, while more efficient, sacrifice this clarity by confounding some interactions with main effects or other interactions. [7, 11]

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Certification Practice Test

Lean Six Sigma Black Belt Improve Phase: DOE Questions and Answers