Design of Experiments (DOE) is a structured method for determining relationships between factors affecting a process and the outputs of that process. One critical approach in DOE is the use of Screening Designs. This guide covers everything you need to know about screening designs, their purpose, comparison with full factorial designs, their benefits and drawbacks, and various types.
What are Screening Designs?
Screening designs are a specific type of DOE intended to efficiently identify the critical factors among many possible variables that influence a process outcome. They help to quickly and economically determine which factors have significant impacts, allowing further detailed analysis to be focused only on these important variables.
Purpose of Screening Designs
The main objectives of screening designs are:
- To identify the most influential factors among a large set.
- To eliminate trivial or insignificant factors early in the experimental phase.
- To optimize resources and time by reducing complexity and focusing subsequent experiments only on important factors.
Screening Designs vs. Full Factorial Designs
Screening Designs:
- Often fractional factorial, using only a subset of the total possible combinations of factor levels.
- Efficient and economical, especially when dealing with many variables.
- Ideal for initial phases of experimentation.
Full Factorial Designs:
- Investigate every possible combination of factor levels.
- Provide comprehensive data on all main effects and interactions.
- Require significantly more resources and experimental runs, which can be impractical with many variables.
Comparison Summary:
- Complexity: Screening (low) vs. Full factorial (high)
- Cost and Time: Screening (efficient) vs. Full factorial (resource-intensive)
- Depth of Insights: Screening (surface level) vs. Full factorial (detailed)
Benefits of Screening Designs
- Efficiency: Quickly identifies influential factors, saving significant experimental resources.
- Cost-effective: Requires fewer experimental runs compared to full factorial designs.
- Focus: Enables detailed analysis only on significant factors.
Drawbacks of Screening Designs
- Limited Interaction Insights: May not fully detect or analyze all interactions between factors.
- Risk of Missing Important Factors: If the design is too aggressive, it might omit crucial factors or interactions.
- Reduced Resolution: Some important interactions may be confounded with main effects.
Types of Screening Designs
1. Fractional Factorial Designs
These designs use a fraction of the full factorial experiment. The fraction is determined by the resolution, indicating the level of confounding:
- Resolution III: Main effects confounded with two-factor interactions.
- Resolution IV: Main effects clear, two-factor interactions may be confounded with each other.
- Resolution V and higher: Main effects and two-factor interactions clearly estimated without confounding.
Example Formula (number of runs for a fractional factorial):
$$\text{Number of runs} = 2^{k-p}$$
where k is the number of factors, and pp is the fractionation level.
2. Plackett-Burman Designs
These designs are highly economical for screening large numbers of factors with relatively few experimental runs. They efficiently identify main effects but heavily confound interactions.
Number of runs typically is:
$$\text{Number of runs} = 4n$$
where n is any integer (e.g., for 7 factors, typically 8 runs are used).
Plackett-Burman designs are particularly advantageous when screening many factors (e.g., 7 or more), as they require fewer runs compared to fractional factorial designs.
3. Definitive Screening Designs (DSD)
Introduced by Jones and Nachtsheim, DSDs efficiently screen factors while estimating quadratic effects and interactions. While a general approximation is:
$$\text{Number of runs} \approx 2k + 1$$
Minitab provides specific run requirements based on the number of factors for definitive screening designs:
| Number of Factors | Number of Runs |
|---|---|
| 2–6 | 13 |
| 7–8 | 17 |
| 9–10 | 21 |
| 11–12 | 25 |
| 13–14 | 29 |
| 15–16 | 33 |
| 17–18 | 37 |
| 19–20 | 41 |
| 21–24 | 49 |
| 25–26 | 53 |
| 27–30 | 61 |
| 31–32 | 65 |
| 33–38 | 77 |
| 39–42 | 85 |
| 43–44 | 89 |
| 45–48 | 97 |
These counts are for designs with all continuous variables. For categorical variables, one additional run is added per replicate. DSDs provide an excellent balance between identifying main effects and modeling curvature with relatively few runs.
Practical Example of a Screening Design
Consider a process with 7 factors. A full factorial design would require:
$$2^7 = 128 \text{ runs}$$
A fractional factorial (Resolution IV) could reduce this to:
$$2^{7-3} = 16 \text{ runs}$$
A Plackett-Burman design could screen these factors in just:
$$8 \text{ runs}$$
While a Definitive Screening Design, based on Minitab's recommendation, would need:
$$17 \text{ runs}$$
These approaches greatly reduce resource requirements while still effectively identifying critical factors.
Conclusion
Screening designs are powerful tools within DOE to quickly and effectively identify significant factors affecting process performance. They are particularly valuable when resources are limited or numerous potential factors exist. Although they may not provide complete insights into all interactions, their ability to streamline experimentation is unmatched, providing essential initial guidance for subsequent, more detailed experimental investigations.