Six Sigma projects often involve more data than a team can easily analyze. A process may have dozens of measurements, inputs, outputs, and quality characteristics. As a result, analysts need methods that simplify complex data without losing important information. One useful method is the scree plot.
A scree plot helps Six Sigma practitioners decide how many principal components to retain during Principal Component Analysis (PCA). PCA reduces many correlated variables into a smaller set of components. The scree plot then provides a visual way to determine where the important variation ends and the smaller contributions begin.
This makes scree plots particularly useful when a Six Sigma team faces a large number of related variables.
For example, a manufacturing process might track temperature, pressure, flow rate, feed rate, motor speed, power consumption, residence time, moisture, particle size, and several quality characteristics. Many of these measurements may correlate with one another. An analyst could study each variable separately. However, that approach may create unnecessary complexity.
PCA can reduce the dimensionality of the data. A scree plot can then help determine how many components provide enough information to keep.
In this article, we will examine how to use a scree plot in Six Sigma, how to interpret the elbow, how it supports DMAIC, and how to avoid common mistakes.
What Is a Scree Plot?
A scree plot is a graph that displays the eigenvalues associated with principal components in descending order. The x-axis shows the component number. The y-axis usually shows the eigenvalue or the amount of variance explained by each component.
The graph often starts with a steep decline. Then, the curve begins to flatten. The point where the steep decline changes into a relatively flat pattern creates the elbow.
The components before the elbow usually contain most of the useful variation. Components after the elbow often contribute much less.
| Scree plot element | Meaning |
|---|---|
| X-axis | Principal component number |
| Y-axis | Eigenvalue or variance explained |
| Steep section | Components explaining substantial variation |
| Elbow | Potential stopping point |
| Flat section | Components adding relatively little information |
| First components | Usually the most important components |
The term “scree” comes from the appearance of loose rock accumulating at the bottom of a steep slope. The plot often resembles that shape.
Most importantly, a scree plot does not replace statistical judgment. Instead, it gives the analyst a practical visual tool for deciding how many components to retain.
Why Do Six Sigma Teams Use Scree Plots?
Six Sigma focuses on reducing variation and improving process performance. However, modern processes can generate hundreds of measurements.
That creates a problem.
More variables do not automatically produce better decisions.
In fact, too many variables can make analysis harder. They can also create multicollinearity, duplicate information, and unnecessary complexity.
PCA addresses this problem by transforming correlated variables into a smaller number of uncorrelated principal components. The first component captures the greatest possible amount of variance. The second captures the greatest remaining variance while remaining orthogonal to the first. Subsequent components continue the process.
A scree plot helps determine how far that process should go.
Consider a process with 15 correlated measurements. PCA may produce 15 components. Yet perhaps the first three explain most of the variation.
Instead of working with 15 variables, the Six Sigma team can investigate three components.
That reduction can make the analysis easier to visualize and explain.
Scree Plots and Data Reduction
Data reduction can support several Six Sigma activities.
For example, teams can use PCA and scree plots to:
- Reduce the number of process variables.
- Identify dominant sources of variation.
- Simplify multivariate datasets.
- Prepare data for additional analysis.
- Detect groups of related measurements.
- Support process monitoring.
- Improve visualization.
- Simplify regression or classification models.
Therefore, the scree plot serves as a decision aid within a broader statistical analysis.
Understanding Principal Components Before Reading a Scree Plot
You cannot interpret a scree plot effectively without understanding PCA.
Suppose a Six Sigma team measures five process variables:
- Temperature
- Pressure
- Flow rate
- Motor speed
- Power consumption
These variables may not operate independently.
For example, higher motor speed may increase flow rate. Higher flow may affect pressure. Motor speed may also increase power consumption.
Consequently, the dataset contains overlapping information.
PCA creates new variables called principal components. Each component combines the original variables using coefficients called loadings.
The first component captures the largest amount of variation. The second captures the next largest amount. The remaining components capture progressively smaller amounts.
The total variance remains distributed across the components. Therefore, the analyst can examine how much variation each component explains.
That information forms the basis of the scree plot.
What Does an Eigenvalue Mean?
The eigenvalue represents the amount of variance associated with a principal component.
When analysts perform PCA using a correlation matrix, each standardized input variable has a variance of one. Consequently, the total variance equals the number of variables.
For example, five standardized variables have total variance of five.
Suppose PCA produces these eigenvalues:
| Component | Eigenvalue | Variance explained |
| PC1 | 2.80 | 56.0% |
| PC2 | 1.20 | 24.0% |
| PC3 | 0.55 | 11.0% |
| PC4 | 0.30 | 6.0% |
| PC5 | 0.15 | 3.0% |
| Total | 5.00 | 100% |
PC1 explains 56% of the variation. PC2 explains another 24%.
Together, the first two components explain 80%.
The remaining three components explain only 20%.
A scree plot would show a substantial decline between PC1 and PC2. It would then show smaller eigenvalues for the remaining components.
That pattern suggests that the first two components may provide a useful reduced representation of the data.
How to Read a Scree Plot
Reading a scree plot involves looking for a change in slope.
A typical pattern looks like this:
Large eigenvalues → steep decline → elbow → gradual decline
Minitab describes the ideal pattern as a steep curve followed by a bend and then a relatively straight line.
The key question is:
Where does the curve stop dropping sharply?
Suppose a scree plot produces these eigenvalues:
| Component | Eigenvalue | Change from previous component |
| PC1 | 4.20 | — |
| PC2 | 2.10 | 2.10 |
| PC3 | 1.15 | 0.95 |
| PC4 | 0.48 | 0.67 |
| PC5 | 0.39 | 0.09 |
| PC6 | 0.34 | 0.05 |
| PC7 | 0.30 | 0.04 |
| PC8 | 0.28 | 0.02 |
The largest changes occur early.
After PC4, the eigenvalues become relatively similar. Therefore, the elbow may occur around PC4.
The analyst could investigate the first four components.
However, the scree plot should not provide the only justification. Analysts should also examine cumulative variance, component loadings, subject-matter knowledge, and other retention methods.
The Elbow Method
The elbow method provides the central idea behind a scree plot.
Imagine dropping a ball down a steep hill. The curve initially falls quickly. Then it reaches a point where the slope becomes much flatter.
That bend represents the elbow.
In PCA, the elbow suggests that additional components provide diminishing returns.
For example:
| Component | Variance explained |
| PC1 | 48% |
| PC2 | 25% |
| PC3 | 13% |
| PC4 | 5% |
| PC5 | 3% |
| PC6 | 2% |
| PC7 | 2% |
| PC8 | 2% |
The first three components explain 86% of the variation.
After PC3, the individual contributions become much smaller.
Therefore, PC3 may represent the elbow.
However, the elbow can sometimes appear ambiguous. Different analysts may select slightly different stopping points. Statistical guidance also notes that choosing the number of components remains partly subjective.
For that reason, Six Sigma teams should combine the scree plot with other evidence.
Scree Plots and Cumulative Variance
Cumulative variance provides another useful decision criterion.
The cumulative variance tells you how much total variation the retained components explain together.
For example:
| Component | Individual variance | Cumulative variance |
| PC1 | 45% | 45% |
| PC2 | 27% | 72% |
| PC3 | 12% | 84% |
| PC4 | 6% | 90% |
| PC5 | 3% | 93% |
| PC6 | 2% | 95% |
A Six Sigma team might decide that four components provide a useful balance because they explain 90% of the variation.
Another project might require only 80%.
Therefore, the appropriate threshold depends on the purpose of the analysis.
Some PCA guidance uses 80% to 90% as a practical reference range, but this should not become a rigid rule.
A process engineer should always consider what information the discarded components contain.
Scree Plot vs. Kaiser Criterion
The Kaiser criterion offers another common method for selecting components.
The rule says to retain components with eigenvalues greater than one when PCA uses standardized variables and the correlation matrix. The logic is simple. Each standardized original variable contributes one unit of variance. Therefore, a component with an eigenvalue greater than one explains more variance than one original variable.
Consider this example:
| Component | Eigenvalue | Kaiser decision |
| PC1 | 3.40 | Keep |
| PC2 | 1.70 | Keep |
| PC3 | 1.10 | Keep |
| PC4 | 0.72 | Drop |
| PC5 | 0.48 | Drop |
| PC6 | 0.30 | Drop |
The Kaiser criterion suggests retaining three components.
However, the Kaiser criterion should not automatically override the scree plot. Research and statistical guidance caution that the rule can produce an excessive number of components in some situations.
Instead, use it as another piece of evidence.
Scree Plots in the Six Sigma DMAIC Framework
A scree plot can support several phases of DMAIC: Define, Measure, Analyze, Improve, and Control.
Define
The Define phase establishes the problem and project goals.
At this stage, the team may identify dozens of potential process variables.
The scree plot normally does not play a major role yet. However, the team can anticipate the need for multivariate analysis if the process contains many correlated measurements.
For example, a battery-material manufacturing project may track numerous process conditions and quality characteristics.
The project team can define a goal such as:
Identify the major combinations of process variables that explain variation in final product quality.
That objective creates a natural role for PCA later.
Measure
The Measure phase focuses on collecting reliable data.
This phase matters greatly because PCA depends on the quality of the input data.
Before creating a scree plot, the team should verify the measurement system and examine the dataset.
Check for:
- Missing values.
- Data-entry errors.
- Extreme outliers.
- Inconsistent units.
- Sampling problems.
- Measurement-system issues.
- Strongly skewed variables.
- Variables measured on very different scales.
Standardization also deserves attention.
If variables have very different units or scales, analysts often use a correlation matrix or standardized variables. Minitab notes that PCA can use covariance or correlation matrices, and the choice affects the interpretation of the eigenvalues.
Analyze
The Analyze phase provides the strongest application for scree plots.
Here, the team can use PCA to reduce dimensionality.
First, the analyst performs PCA.
Next, the software calculates eigenvalues.
Then, the analyst creates the scree plot.
Finally, the team identifies a reasonable number of components.
For example, a process contains 12 correlated measurements. PCA shows that the first three components explain 82% of the variation.
The scree plot also shows a clear elbow after PC3.
Now the team has evidence that three components capture most of the meaningful structure.
The team can then examine the loadings for those three components.
Improve
During Improve, the team uses the analytical findings to target process changes.
Suppose PC1 has strong positive loadings for temperature, energy input, and residence time.
That pattern may indicate a common process condition.
Meanwhile, PC2 may have strong loadings for feed rate and pressure.
The team can then investigate these combinations rather than treating every variable as an independent problem.
This can simplify experimentation.
For example, the team could use the retained components to help identify factors for a designed experiment.
However, the team should return to the original process variables before implementing changes. Principal components are mathematical combinations. They do not automatically represent physical causes.
Control
The Control phase focuses on sustaining improvements.
The retained components can sometimes support ongoing monitoring.
A team might monitor PC scores instead of tracking every highly correlated variable independently.
For example, suppose 10 measurements describe related characteristics of a process. PCA reduces them to three important components.
The team could monitor those components for unusual changes.
Minitab notes that score plots can help identify clusters, trends, and potential outliers when the first components capture most of the variance.
Still, the control plan should retain appropriate individual measurements where they have direct process or customer significance.
Practical Six Sigma Example
Consider a chemical manufacturing process.
The engineering team collects eight measurements:
| Variable | Description |
| X1 | Reactor temperature |
| X2 | Reactor pressure |
| X3 | Feed rate |
| X4 | Agitator speed |
| X5 | Energy consumption |
| X6 | Residence time |
| X7 | Moisture |
| X8 | Particle size |
The variables show substantial correlation.
The team performs PCA.
The resulting eigenvalues are:
| Component | Eigenvalue | Variance explained | Cumulative |
| PC1 | 3.60 | 45.0% | 45.0% |
| PC2 | 1.80 | 22.5% | 67.5% |
| PC3 | 1.05 | 13.1% | 80.6% |
| PC4 | 0.55 | 6.9% | 87.5% |
| PC5 | 0.40 | 5.0% | 92.5% |
| PC6 | 0.30 | 3.8% | 96.3% |
| PC7 | 0.20 | 2.5% | 98.8% |
| PC8 | 0.10 | 1.3% | 100% |
The scree plot shows a strong decline through PC3 and then a much flatter pattern.
The elbow therefore appears around PC3.
The first three components explain approximately 81% of the total variation.
The Kaiser criterion also supports retaining the first three components because their eigenvalues exceed one.
That provides stronger evidence than either method alone.
Next, the team examines the loadings.
Suppose PC1 strongly relates to temperature, energy consumption, and residence time.
The engineers may interpret PC1 as a general thermal-process condition.
PC2 may strongly relate to feed rate and pressure.
The team might interpret PC2 as a throughput condition.
PC3 may strongly relate to moisture and particle size.
That component may represent a product-quality dimension.
The team now has a much simpler view of the process.
Instead of interpreting eight variables independently, it can investigate three major patterns.
What a Scree Plot Cannot Tell You
A scree plot can identify how much variation each component captures.
However, it cannot tell you what physically causes the variation.
That requires additional analysis.
For example, PC1 might explain 50% of the variation. That does not mean PC1 represents a specific physical mechanism.
You must examine the loadings.
Likewise, a large eigenvalue does not automatically mean that a component represents a critical-to-quality characteristic.
Six Sigma teams must connect statistical results with process knowledge.
Therefore, use the scree plot as a screening and dimension-reduction tool, not as proof of causation.
Common Mistakes When Using Scree Plots
Several mistakes can reduce the value of a scree plot.
Mistake 1: Treating the Elbow as an Exact Answer
The elbow can be subjective.
If the curve gradually flattens, analysts may disagree about the correct number of components.
Therefore, compare the scree plot with cumulative variance and other methods.
Mistake 2: Automatically Keeping Eigenvalues Above One
The Kaiser criterion provides a useful rule of thumb. However, it should not become an automatic decision.
Use the scree plot and process knowledge as additional evidence.
Mistake 3: Ignoring Variable Scaling
A temperature measurement and a pressure measurement may have very different units and variances.
If the team ignores scale, variables with larger numerical variance can dominate the PCA.
Therefore, determine whether standardization makes sense for the project.
Mistake 4: Ignoring the Loadings
The scree plot tells you how many components may matter.
It does not tell you what those components mean.
Always review the component loadings.
Mistake 5: Assuming More Components Are Better
PCA seeks to simplify the dataset.
Keeping every component defeats that purpose.
The goal is not to maximize the number of components. The goal is to retain enough information to support the project.
Mistake 6: Treating PCA as Causal Analysis
PCA identifies patterns of variation.
It does not establish cause and effect.
Use experiments, regression, process knowledge, and other Six Sigma tools when you need causal evidence.
Using Minitab to Create a Scree Plot
Minitab provides a direct scree plot option within its PCA analysis. The software plots principal components against their corresponding eigenvalues and orders the eigenvalues from largest to smallest.
A typical workflow looks like this:
- Organize the process variables in columns.
- Verify the measurement data.
- Determine whether standardization is appropriate.
- Open the PCA procedure.
- Select the variables.
- Request the scree plot.
- Review eigenvalues.
- Examine cumulative variance.
- Identify the likely elbow.
- Review component loadings.
- Validate the interpretation with process experts.
This approach works well because it combines graphical evidence with statistical output.
Using JMP and Other Software
JMP, R, Python, SAS, and other statistical packages can also generate PCA results and scree plots.
Regardless of the software, the underlying logic remains the same.
The software calculates principal components. It then orders them according to their associated eigenvalues. The analyst evaluates the decline in eigenvalues and determines how many components to retain.
Therefore, the important skill is not knowing where a particular menu item sits.
The important skill is understanding what the plot means.
Scree Plots and Process Improvement
Scree plots become especially valuable when Six Sigma teams face complex processes.
Consider a process with 30 measurements.
Analyzing all 30 variables separately may overwhelm the project team.
PCA might reduce those 30 variables to five components.
The scree plot provides evidence for retaining those five.
Now the team can focus on the dominant patterns.
That reduction can improve communication as well.
Instead of telling management that 30 variables contribute to process variation, the team can explain three or four major dimensions.
The team can then return to the original variables to identify practical improvement opportunities.
In this way, the scree plot helps bridge statistical analysis and process understanding.
When Should You Use a Scree Plot?
A scree plot works best when you have multiple correlated variables and want to reduce dimensionality.
| Situation | Scree plot usefulness |
| Many correlated variables | High |
| Few independent variables | Low |
| Need for PCA | High |
| Simple univariate analysis | Low |
| Data visualization | Moderate to high |
| Variable reduction | High |
| Root-cause confirmation alone | Low |
| Multivariate process analysis | High |
If your dataset contains only two or three variables, PCA may add little value.
On the other hand, a dataset with dozens of correlated measurements can benefit greatly.
Best Practices for Six Sigma Practitioners
Follow these guidelines when using scree plots:
- Start with a clear project question.
- Verify the measurement system first.
- Understand the correlation structure.
- Choose covariance or correlation appropriately.
- Standardize variables when appropriate.
- Create the scree plot after performing PCA.
- Look for the elbow.
- Review cumulative variance.
- Compare the result with the Kaiser criterion.
- Examine component loadings.
- Use process knowledge to interpret components.
- Avoid treating PCA as causal evidence.
- Document why you selected the final number of components.
- Validate important findings with additional analysis.
Most importantly, document the reasoning.
A strong Six Sigma analysis should allow another analyst to understand why the team retained three components rather than four.
Conclusion
Scree plots provide a simple visual method for solving an important Six Sigma problem: how many principal components should we keep?
The plot displays the eigenvalues in descending order. Analysts then look for the point where the curve changes from steep to relatively flat. That point creates the elbow.
However, the elbow should not stand alone.
A strong analysis combines the scree plot with cumulative variance, eigenvalues, component loadings, and process knowledge. The Kaiser criterion can also provide a useful comparison, although it should not serve as the only decision rule.
Within DMAIC, scree plots are especially valuable during the Analyze phase. They can also support Measure, Improve, and Control when teams need to understand or monitor complex multivariate processes.
Ultimately, the purpose is not simply to create an attractive graph.
The purpose is to simplify complex data while preserving the information that matters.
When used correctly, a scree plot helps Six Sigma practitioners reduce dimensionality, identify dominant patterns, improve statistical analysis, and communicate complex process variation more clearly.
That makes the scree plot a valuable companion to PCA and a practical tool for modern Six Sigma projects.
