Lean Six Sigma Black Belt Improve Phase: DOE Questions and Answers — 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?
- Response Surface Methodology (RSM)
- A screening design, such as a fractional factorial (Correct answer)
- A full factorial design with fewer factors
- One-Factor-at-a-Time (OFAT) experimentation
Correct answer: A screening design, such as a fractional factorial
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?
- Main effects are confounded with other main effects.
- No main effects are confounded with two-factor interactions.
- Main effects are confounded with two-factor interactions. (Correct answer)
- Two-factor interactions are confounded with other two-factor interactions.
Correct answer: Main effects are confounded with two-factor interactions.
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?
- To increase the number of factors that can be studied.
- To reduce the total number of experimental runs required.
- To allow the experiment to be run over multiple days.
- To check for curvature in the relationship between factors and the response. (Correct answer)
Correct answer: To check for curvature in the relationship between factors and the response.
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?
- Replication
- Randomization
- Blocking (Correct answer)
- Confounding
Correct answer: Blocking
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?
- It requires fewer resources and experimental runs.
- It is the most effective design for screening a large number of factors.
- It allows for the estimation of all main effects and all interaction effects, free from confounding. (Correct answer)
- It can only be used to study linear relationships between variables.
Correct answer: It allows for the estimation of all main effects and all interaction effects, free from confounding.
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]
Question 6: A project team is conducting a DOE to optimize the yield of a chemical process. They have identified three critical factors. Their goal is to not only understand the main effects and interactions but also to model potential curvature in the response to find the precise optimal settings. Which experimental design approach is most suitable?
- A Resolution III fractional factorial design
- A Plackett-Burman screening design
- Response Surface Methodology (RSM) (Correct answer)
- A Taguchi L4 array
Correct answer: Response Surface Methodology (RSM)
Response Surface Methodology (RSM), such as a Central Composite Design, is used for process optimization when the goal is to find the specific factor settings that maximize or minimize a response. [4, 22] RSM designs include axial and center points, which allow for the modeling of quadratic effects (curvature), which is essential for fine-tuning and finding the true optimum. [4, 20]
Lean Six Sigma Black Belt Improve Phase: DOE Questions and Answers
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?