Six Sigma projects often involve many variables. A manufacturing process may have dozens of inputs. A customer survey may contain hundreds of questions. A quality study may track temperature, pressure, speed, flow rate, cycle time, and several other factors.
However, more data does not always create better decisions.
Too many variables can make analysis difficult. They can also hide important relationships. Principal component analysis (PCA) provides one way to simplify these complex datasets. It combines correlated variables into a smaller set of principal components.
The next question becomes important: How many principal components should you keep?
The Kaiser criterion provides one common answer.
The Kaiser criterion, also called the eigenvalue-greater-than-one rule, recommends retaining principal components with eigenvalues greater than 1 when PCA uses a correlation matrix. Minitab identifies this as one method for determining the number of principal components to retain.
This rule can help Six Sigma practitioners reduce dimensionality without immediately relying on subjective judgment. Moreover, it works well as an initial screening method.
Still, the Kaiser criterion should not operate alone. Analysts should compare it with a scree plot, cumulative variance, and process knowledge. The rule can retain too many components in some datasets. Therefore, Six Sigma teams should use it as evidence rather than as an automatic final decision.
This article explains how the Kaiser criterion works, where it fits into Six Sigma, and how to apply it using practical examples.
What Is the Kaiser Criterion?
The Kaiser criterion is a rule for deciding how many principal components or factors to retain.
The basic rule is simple:
Retain components with eigenvalues greater than 1.
An eigenvalue represents the variance explained by a principal component. When PCA uses standardized variables and a correlation matrix, each original variable contributes a variance of 1.
Therefore, an eigenvalue greater than 1 means that a component explains more variance than one standardized original variable.
For example, suppose a PCA produces these eigenvalues:
| Component | Eigenvalue | Kaiser Decision |
|---|---|---|
| PC1 | 3.85 | Retain |
| PC2 | 2.10 | Retain |
| PC3 | 1.42 | Retain |
| PC4 | 0.87 | Reject |
| PC5 | 0.46 | Reject |
| PC6 | 0.30 | Reject |
The first three components have eigenvalues above 1.
Therefore, the Kaiser criterion recommends retaining three principal components.
The logic comes from comparing each component with the variance contributed by one standardized variable. NIST describes the rule as retaining eigenvalues larger than unity.
Why Does an Eigenvalue of 1 Matter?
The value 1 becomes important because standardized variables have a variance of 1.
Imagine a Six Sigma project that studies eight process variables:
- Temperature
- Pressure
- Flow rate
- Feed rate
- Residence time
- Motor speed
- Energy consumption
- Product yield
After standardization, each variable has a variance of approximately 1.
The total variance therefore equals approximately 8.
PCA redistributes that variance across the principal components.
For example:
| Component | Eigenvalue | Variance Explained |
| PC1 | 3.20 | 40.0% |
| PC2 | 2.10 | 26.3% |
| PC3 | 1.15 | 14.4% |
| PC4 | 0.65 | 8.1% |
| PC5 | 0.40 | 5.0% |
| PC6 | 0.25 | 3.1% |
| PC7 | 0.15 | 1.9% |
| PC8 | 0.10 | 1.3% |
The total equals 8.
PC1 explains the equivalent variance of 3.2 standardized variables. PC2 explains 2.1 variables’ worth of variance. PC3 explains 1.15 variables’ worth.
However, PC4 explains less variance than a single standardized variable.
Consequently, the Kaiser criterion retains PC1, PC2, and PC3.
Minitab similarly defines eigenvalues as the variances of principal components.
Kaiser Criterion and Principal Component Analysis
The Kaiser criterion fits naturally within PCA.
PCA transforms correlated variables into a smaller number of uncorrelated components. The first component explains the greatest amount of variation. The second component explains the next greatest amount. Each later component explains progressively less variation.
This structure makes PCA useful in Six Sigma.
A project might begin with 20 process variables. Yet many of those variables may measure similar underlying behavior.
For example, temperature measurements taken at several points may move together. Likewise, pressure, flow, and energy consumption may show strong relationships.
PCA can combine these variables into a few components.
The Kaiser criterion then provides a straightforward way to determine how many components deserve further attention.
Basic PCA workflow
A typical workflow looks like this:
- Collect the process data.
- Clean the dataset.
- Standardize variables when appropriate.
- Calculate the correlation matrix.
- Perform PCA.
- Review eigenvalues.
- Apply the Kaiser criterion.
- Examine the scree plot.
- Review cumulative variance.
- Interpret component loadings.
- Validate the result with process knowledge.
- Use the selected components in further analysis.
This approach fits well within the Analyze phase of DMAIC.
Using the Kaiser Criterion in Six Sigma
The Kaiser criterion can support several Six Sigma activities.
It can help teams simplify process data. It can also support root cause analysis, multivariate analysis, measurement studies, and process optimization.
The following table summarizes several applications.
| Six Sigma Application | How Kaiser Criterion Helps |
| Process optimization | Reduces many correlated process variables |
| Root cause analysis | Groups related sources of variation |
| Multivariate analysis | Reduces the number of predictor variables |
| Customer analysis | Simplifies large survey datasets |
| Measurement studies | Identifies dominant patterns among measurements |
| Process monitoring | Creates fewer composite variables |
| DOE interpretation | Helps summarize correlated responses |
| Predictive modeling | Can reduce model complexity |
| Manufacturing analysis | Groups related process conditions |
| Quality improvement | Highlights major variation patterns |
The key benefit involves dimensionality reduction.
Instead of analyzing 20 highly correlated variables independently, a Six Sigma team might analyze four principal components.
That can make the process easier to understand.
Kaiser Criterion in the DMAIC Methodology
The Kaiser criterion fits particularly well into the Analyze phase of DMAIC.
However, teams can use PCA before and after Analyze when the project requires it.
Define
During Define, the team establishes the problem and project scope.
At this stage, the Kaiser criterion usually has little direct use. However, the team can identify whether the project contains a large multivariate dataset.
For example, a project might investigate excessive variation in a chemical manufacturing process.
The team may track 25 process variables.
That number suggests that dimensionality reduction could become useful later.
Measure
During Measure, the team collects reliable data.
The team should confirm measurement quality before applying PCA. Poor measurement systems can create misleading relationships.
For example, suppose a temperature sensor has poor repeatability. PCA may identify a pattern associated with that sensor. However, the pattern may represent measurement noise rather than process behavior.
Therefore, measurement system analysis remains important.
Analyze
This phase provides the strongest application for the Kaiser criterion.
The team can perform PCA and examine the eigenvalues.
Suppose the project contains 12 variables.
The PCA produces:
| Component | Eigenvalue | Cumulative Variance |
| PC1 | 4.20 | 35.0% |
| PC2 | 2.80 | 58.3% |
| PC3 | 1.70 | 72.5% |
| PC4 | 1.15 | 82.1% |
| PC5 | 0.78 | 88.6% |
| PC6 | 0.51 | 92.8% |
The Kaiser criterion retains four components.
The team can then examine the loadings for those four components.
Improve
The selected components can help the team identify improvement opportunities.
For instance, PC1 may combine several variables related to heating. PC2 may represent material flow. PC3 may capture equipment speed. PC4 may capture environmental conditions.
The team can then focus improvement work on these broader drivers.
Control
Finally, the team may monitor the selected components.
Instead of monitoring 12 correlated variables separately, the team could track several meaningful component scores.
However, the team should only do this when the components have a clear operational interpretation.
Practical Example: Manufacturing Process
Consider a manufacturing process with eight process variables.
The Six Sigma team wants to understand the major sources of variation.
The variables include:
- Temperature
- Pressure
- Flow rate
- Feed rate
- Motor speed
- Energy use
- Residence time
- Cooling rate
The team performs PCA using the correlation matrix.
The results appear below.
| Component | Eigenvalue | % Variance | Cumulative % |
| PC1 | 3.10 | 38.8% | 38.8% |
| PC2 | 1.95 | 24.4% | 63.2% |
| PC3 | 1.32 | 16.5% | 79.7% |
| PC4 | 0.78 | 9.8% | 89.5% |
| PC5 | 0.40 | 5.0% | 94.5% |
| PC6 | 0.25 | 3.1% | 97.6% |
| PC7 | 0.12 | 1.5% | 99.1% |
| PC8 | 0.07 | 0.9% | 100.0% |
The first three eigenvalues exceed 1.
Therefore, the Kaiser criterion recommends three components.
The first three components explain 79.7% of total variation.
That result gives the team a useful starting point.
Interpreting the Principal Components
Selecting components represents only the first step.
Next, the team must determine what each component means.
Suppose the loading table looks like this:
| Variable | PC1 | PC2 | PC3 |
| Temperature | 0.89 | 0.12 | 0.08 |
| Pressure | 0.84 | 0.18 | 0.11 |
| Flow rate | 0.76 | 0.31 | 0.15 |
| Feed rate | 0.20 | 0.88 | 0.10 |
| Motor speed | 0.18 | 0.82 | 0.25 |
| Energy use | 0.72 | 0.25 | 0.18 |
| Residence time | 0.15 | 0.22 | 0.86 |
| Cooling rate | 0.12 | 0.10 | 0.91 |
The pattern becomes easier to interpret.
PC1 has strong loadings for temperature, pressure, flow rate, and energy use.
The team might label PC1 Thermal and Pressure Conditions.
PC2 has strong loadings for feed rate and motor speed.
The team might call it Production Rate.
PC3 has strong loadings for residence time and cooling rate.
The team might call it Cooling and Residence Conditions.
Now the PCA result becomes useful from a process perspective.
Instead of thinking about eight separate variables, the team can investigate three broader process patterns.
Minitab recommends examining the magnitude and direction of coefficients when interpreting principal components. Larger absolute coefficients indicate greater importance in calculating the component.
Kaiser Criterion vs. Scree Plot
The Kaiser criterion and scree plot often work together.
The Kaiser criterion uses a numerical cutoff.
The scree plot provides a visual assessment.
A scree plot orders eigenvalues from largest to smallest. Analysts then look for the point where the curve begins to flatten. Minitab describes this bend as a common way to identify the useful components before the eigenvalues form a flatter pattern.
Consider this example:
| Component | Eigenvalue |
| PC1 | 4.30 |
| PC2 | 2.30 |
| PC3 | 1.40 |
| PC4 | 1.05 |
| PC5 | 0.91 |
| PC6 | 0.82 |
| PC7 | 0.75 |
| PC8 | 0.72 |
The Kaiser criterion retains four components.
However, the scree plot might show a clear bend after PC3.
That creates a decision point.
Should the team retain three or four?
The answer should depend on the project’s objective.
If PC4 explains little additional variation and has weak process interpretation, three components may make more sense.
On the other hand, if PC4 captures an important quality mechanism, the team may retain it.
Therefore, the Kaiser criterion should not replace engineering judgment.
Kaiser Criterion vs. Cumulative Variance
Cumulative variance provides another useful check.
Suppose a PCA produces:
| Components Retained | Cumulative Variance |
| 1 | 42% |
| 2 | 65% |
| 3 | 78% |
| 4 | 86% |
| 5 | 91% |
The Kaiser criterion may recommend four components.
Those four components explain 86% of the total variation.
That result may work well for descriptive analysis.
However, the required variance level depends on the application. Minitab notes that analysts may use around 80% for some descriptive applications and may seek at least 90% for some downstream analyses.
Consequently, Six Sigma teams should define what “enough” means before selecting the final number.
A Complete Kaiser Criterion Example
Imagine a Six Sigma team studying customer complaints.
The team collects data from 500 customers.
The survey contains 15 questions covering:
- Product reliability
- Ease of use
- Delivery
- Customer service
- Product appearance
- Documentation
- Pricing
- Technical support
- Warranty experience
The team wants to reduce the 15 variables into a smaller number of dimensions.
PCA produces these eigenvalues:
| Component | Eigenvalue | % Variance |
| PC1 | 4.60 | 30.7% |
| PC2 | 2.80 | 18.7% |
| PC3 | 1.90 | 12.7% |
| PC4 | 1.25 | 8.3% |
| PC5 | 0.92 | 6.1% |
| PC6 | 0.71 | 4.7% |
| PC7 | 0.58 | 3.9% |
| PC8 | 0.46 | 3.1% |
The remaining components have even smaller eigenvalues.
The Kaiser criterion therefore recommends four components.
The cumulative variance equals:
30.7% + 18.7% + 12.7% + 8.3% = 70.4%
The team then reviews the loadings.
PC1 may represent Product Performance.
PC2 may represent Customer Support.
PC3 may represent Delivery Experience.
PC4 may represent Commercial Value.
The team now has four interpretable dimensions instead of 15 survey variables.
This simplified structure can make further Six Sigma analysis much easier.
Advantages of the Kaiser Criterion
The Kaiser criterion offers several benefits.
1. It is easy to understand
The rule uses a simple threshold.
Retain eigenvalues greater than 1.
That simplicity makes the method accessible to practitioners who do not specialize in multivariate statistics.
2. It provides an objective starting point
Without a retention rule, analysts might choose components based entirely on judgment.
The Kaiser criterion provides an initial numerical recommendation.
3. It works well with PCA
PCA already produces eigenvalues.
Therefore, the team does not need a separate complicated calculation.
4. It reduces complexity
The method can help reduce dozens of variables to a smaller set of components.
That reduction can improve visualization and downstream modeling.
5. It supports Six Sigma problem solving
The resulting components can reveal broad patterns in process variation.
Consequently, teams can focus improvement efforts on major sources of variation.
Limitations of the Kaiser Criterion
Despite its simplicity, the Kaiser criterion has important limitations.
It Can Retain Too Many Components
This represents one of the biggest concerns.
Research has shown that the rule can identify eigenvalues above 1 even in random datasets. One study notes that the criterion can overestimate the number of meaningful components, particularly when many variables lack strong correlations.
Therefore, teams should avoid treating the rule as a guaranteed statistical truth.
It Depends on Data Scaling
The value of 1 has a clear interpretation when analysts standardize variables and use the correlation matrix.
However, covariance-based PCA can produce very different eigenvalues when variables have different units or scales.
Minitab notes that PCA can use either correlation or covariance matrices. With the correlation matrix approach, standardized data form the basis of the analysis.
Therefore, analysts must understand which matrix they used.
It Ignores Process Meaning
A component can have an eigenvalue below 1 and still contain useful information.
For example, a small component might represent a rare but critical failure mode.
Six Sigma focuses on improving processes, not simply maximizing statistical compression.
Therefore, process knowledge matters.
It Can Depend on Sample Characteristics
Sampling variation can affect eigenvalues.
As a result, a component may fall just above or below the threshold.
For example, an eigenvalue of 1.02 should not automatically receive much more attention than one of 0.98.
The difference is small.
How to Use the Kaiser Criterion Correctly
A strong Six Sigma approach combines several pieces of evidence.
Use the following sequence:
| Step | Action |
| 1 | Verify the measurement system |
| 2 | Examine correlations |
| 3 | Standardize variables when appropriate |
| 4 | Run PCA |
| 5 | Review eigenvalues |
| 6 | Apply the Kaiser criterion |
| 7 | Examine the scree plot |
| 8 | Review cumulative variance |
| 9 | Interpret loadings |
| 10 | Check process knowledge |
| 11 | Validate the selected components |
| 12 | Document the decision |
This approach prevents one simple rule from driving the entire analysis.
Kaiser Criterion in Minitab
Minitab provides eigenvalues, proportions, cumulative proportions, and graphical results as part of PCA interpretation.
A typical workflow involves selecting the variables for the PCA and reviewing the resulting eigenanalysis.
The output may look similar to:
| Component | Eigenvalue | Proportion | Cumulative |
| PC1 | 3.55 | 0.443 | 0.443 |
| PC2 | 2.13 | 0.266 | 0.710 |
| PC3 | 1.04 | 0.131 | 0.841 |
| PC4 | 0.53 | 0.066 | 0.907 |
| PC5 | 0.41 | 0.051 | 0.958 |
In this example, the first three components have eigenvalues greater than 1.
Therefore, the Kaiser criterion recommends three components.
Those three components explain 84.1% of the variation.
Minitab also provides a scree plot and component coefficients to support interpretation.
Kaiser Criterion in JMP
JMP also supports PCA and multivariate analysis workflows.
The general process remains the same.
First, select the variables.
Next, examine the eigenvalues.
Then, identify the components with eigenvalues above 1.
Afterward, review the scree plot and loading structure.
Finally, connect the statistical results to the physical process.
The software can perform the calculations quickly. However, the Six Sigma practitioner still needs to determine whether the components make practical sense.
That distinction matters.
Software can identify patterns.
It cannot determine whether a pattern represents a meaningful process mechanism.
Kaiser Criterion and Root Cause Analysis
PCA can also support root cause analysis.
Suppose a process has 20 correlated variables.
Running separate analyses on all 20 variables may create confusion.
Instead, PCA can identify a smaller number of dominant patterns.
The Kaiser criterion can then help determine how many components to investigate.
For example:
| Component | Main Variables | Possible Process Theme |
| PC1 | Temperature, pressure, energy | Thermal conditions |
| PC2 | Speed, feed rate, cycle time | Production rate |
| PC3 | Cooling, residence time | Heat removal |
| PC4 | Humidity, ambient temperature | Environment |
The Six Sigma team can investigate these four themes rather than treating every variable as an independent root cause.
However, PCA does not prove causation.
That point deserves emphasis.
A strong loading means that variables contribute strongly to a component. It does not prove that one variable causes another.
Teams should use additional tools such as regression, DOE, hypothesis tests, process mapping, and engineering experiments to confirm causes.
When Should Six Sigma Practitioners Use the Kaiser Criterion?
The criterion works best when the project has many related variables and the team needs dimensionality reduction.
It can be particularly useful when:
- Many variables show significant correlation.
- The team needs to simplify a dataset.
- PCA represents a reasonable analytical method.
- Variables use comparable or standardized scales.
- The team needs an initial component-retention rule.
- The resulting components have practical interpretations.
It becomes less useful when the variables have little correlation.
It also becomes less useful when the project requires extremely precise component selection.
In those situations, consider additional retention methods.
Alternatives to the Kaiser Criterion
Six Sigma practitioners have several options.
Scree Plot
The scree plot looks for a bend in the eigenvalue curve.
It provides a visual method and often works well alongside the Kaiser criterion.
Cumulative Variance
This approach retains enough components to explain a chosen percentage of total variance.
The appropriate percentage depends on the project.
Parallel Analysis
Parallel analysis compares observed eigenvalues with eigenvalues generated from random data.
This approach can provide a stronger statistical basis than simply using the value of 1.
Process Knowledge
Sometimes the most useful solution comes from understanding the process.
A component with a slightly smaller eigenvalue may still deserve attention if it represents an important failure mechanism.
The best practice therefore combines statistical evidence with process knowledge.
Kaiser Criterion Best Practices for Six Sigma
Follow these guidelines when applying the method.
Standardize When Appropriate
If variables use different units, consider standardization.
Temperature might use degrees Celsius. Pressure might use psi. Flow might use liters per minute.
Those scales cannot always be compared directly.
Check Correlations First
PCA works best when meaningful relationships exist among variables.
If every variable behaves independently, PCA may provide little value.
Do Not Use the Rule Alone
Always compare the Kaiser result with other evidence.
Use the scree plot and cumulative variance.
Then examine loadings.
Interpret the Components
Do not stop after counting eigenvalues above 1.
Ask what each retained component represents.
Validate the Result
Use the selected components in the next stage of analysis.
Check whether they improve understanding or prediction.
Document the Decision
Record why the team selected the final number of components.
That documentation improves reproducibility and supports the Control phase.
Kaiser Criterion Checklist
A Six Sigma practitioner can use this quick checklist:
| Question | Yes/No |
| Are the variables suitable for PCA? | |
| Did the team review the measurement system? | |
| Did the team examine correlations? | |
| Did the team use an appropriate scaling method? | |
| Did the team calculate eigenvalues? | |
| Did the team apply the eigenvalue > 1 rule? | |
| Did the team review the scree plot? | |
| Did the team examine cumulative variance? | |
| Are the retained components interpretable? | |
| Do the components have process meaning? | |
| Did the team compare alternative retention methods? | |
| Did the team document the final decision? |
This checklist helps prevent mechanical use of the Kaiser criterion.
Conclusion
The Kaiser criterion provides a simple way to decide how many principal components to retain in PCA. Its central rule is straightforward: retain components with eigenvalues greater than 1 when working with standardized variables and a correlation matrix.
For Six Sigma practitioners, that simplicity offers real value.
Complex manufacturing, service, and customer datasets can contain many correlated variables. PCA can compress those variables into a smaller number of components. The Kaiser criterion can then provide an initial estimate of how many components contain substantial variation.
However, the rule has limitations.
It can retain too many components. It can also overlook components that have smaller but practically important variation. Therefore, Six Sigma teams should combine the Kaiser criterion with scree plots, cumulative variance, loading interpretation, and process knowledge.
Most importantly, remember that statistical significance and process importance are not always the same thing.
The best Six Sigma analysis connects both.
Use the Kaiser criterion to simplify the data. Use PCA to reveal patterns. Then use engineering knowledge and additional Six Sigma tools to determine what those patterns actually mean.
That balanced approach turns a simple eigenvalue rule into a useful part of data-driven process improvement.
