A blender manufacturer was losing $800K per year to motor failures. Factor Relationship Diagrams helped them structure an experiment that doubled motor life. Here is the full methodology.
Case Study · 2025-05-12 · 9 min · OpEx Excellence Team
When Experiments Fail, the Design Is Usually the Problem
A consumer blender manufacturer had run three separate DOE studies on motor durability, and none had produced actionable results. Each experiment tested reasonable factors, used proper randomization, and was analyzed correctly. But the results were inconsistent: factors that appeared significant in one study were insignificant in the next. The problem was not the analysis. It was the experimental design. The team was not distinguishing between factors they could easily change between runs and factors that required stopping production to adjust. They were not accounting for noise variables that changed between test sessions. And they were not structuring the relationship between their factors and responses in a way that matched the physical reality.
Enter the Factor Relationship Diagram
A Factor Relationship Diagram (FRD) is a structured visual tool that forces the team to classify every variable before designing the experiment. Each factor gets assigned a role: Design Factor (controllable and easy to change), CRD or Whole Plot Factor (controllable but hard to change), Noise Factor (uncontrollable but measurable), Covariate (measurable background variable), or Response (the outcome you are measuring). For the blender motor, the FRD revealed something the previous experiments had missed. Motor winding temperature was being treated as a controllable factor (set it and forget it), but in practice, it took 45 minutes to stabilize at a new temperature. This made it a whole-plot factor, not a subplot factor. Running it as a subplot factor had invalidated the error structure of all three previous experiments.
If a factor takes significant time or cost to change between runs, it is a whole-plot factor and must be handled with a split-plot design. Treating it as a regular factor inflates the false positive rate.
The Structured Design
With the FRD complete, the team designed a split-plot experiment. Motor winding temperature (hard to change) was the whole-plot factor, run at two levels across four whole plots. Within each whole plot, they tested three subplot factors: brush material, commutator surface finish, and bearing preload. Noise factors (ambient humidity and duty cycle pattern) were measured but not controlled, following a Taguchi inner/outer array philosophy. The FRD made the design structure visible to the entire team. Everyone could see why certain factors were grouped together and why the analysis would use different error terms for whole-plot and subplot effects.
- Whole Plot Factor: Motor winding temperature (2 levels, hard to change)
- Subplot Factors: Brush material (2 levels), commutator finish (2 levels), bearing preload (2 levels)
- Noise Factors: Ambient humidity (measured), duty cycle pattern (measured)
- Responses: Motor life (hours to failure), power efficiency at 1000 hours
The Results That Finally Made Sense
For the first time, the experiment produced clear, reproducible results. The split-plot ANOVA correctly separated whole-plot error from subplot error, revealing effects that had been hidden in the noise of previous experiments. Brush material and bearing preload had a strong interaction: the best brush depended on which preload was used. Motor winding temperature interacted with commutator finish at the whole-plot level. The optimized combination doubled the median motor life from 1,200 hours to 2,450 hours. Confirmation runs validated the results within 5% of predictions.
Why FRD Made the Difference
The Factor Relationship Diagram did not change the statistics. It changed the thinking. By forcing the team to explicitly classify each variable's role, the FRD exposed a design flaw (treating a hard-to-change factor as easy-to-change) that had been silently corrupting their experiments for over a year. The FRD also made the experimental plan communicable. Managers, operators, and technicians could all understand the experiment's structure by looking at the diagram, without needing to read a statistical design matrix.
Frequently Asked Questions
What is a Factor Relationship Diagram?
A Factor Relationship Diagram (FRD) is a visual tool that classifies every variable in an experiment by its role: design factor, whole-plot factor, noise factor, covariate, or response. It structures the relationship between inputs and outputs and determines the correct experimental design type (completely randomized, split-plot, etc.).
What is a split-plot design and when do I need one?
A split-plot design is used when some factors are hard to change (expensive or time-consuming to adjust between runs). These 'hard-to-change' factors are randomized at the whole-plot level while 'easy-to-change' factors are randomized within each whole plot. Using a split-plot design when you have hard-to-change factors ensures your statistical tests have the correct error terms.
Can I build FRDs in OpEx Excellence?
Yes. OpEx Excellence includes an interactive FRD builder that lets you classify factors by role, define their levels, and automatically generates the correct experimental design structure based on your factor classifications.
Build your own FRD
Try the interactive Factor Relationship Diagram tool. Classify your factors, define your design structure, and generate the experiment matrix automatically.
Get started →Tags: FRD, factor relationship diagram, blender, motor life, DOE, split-plot design