Kurtosis and Skewness in asset management are complementary statistical metrics that reveal how a signal’s shape and symmetry deviate from normal behavior.
When reliability engineers apply these features to vibration, acoustic, or process data, they can detect impulses and asymmetries early, diagnose faults more accurately, and improve maintenance decisions.
Consequently, organizations reduce unplanned downtime, boost asset availability, and strengthen safety.
Why Kurtosis and Skewness matter in asset management
In modern asset management, data-driven insights help balance cost, risk, and performance across the entire asset lifecycle.
While quantitative metrics like peak, peak-to-peak, and RMS are essential, you can also extract distribution-based features that characterize signal shape and asymmetry.
Therefore, incorporating Kurtosis and Skewness into your vibration analysis workflow provides early-warning sensitivity to impulsive events and directional bias — key indicators of emerging mechanical defects.
Beyond Peak and RMS: Shape-based metrics
In addition to well-known quantitative metrics previously discussed on our blog (peak, peak-to-peak, RMS), it is possible — and beneficial — to derive metrics that describe the shape and asymmetry of a waveform.
Because a digital signal is formed by discrete time points, any vibration series can be treated as a statistical distribution of acceleration, velocity, or displacement.
Vibration signals and the Gaussian Curve
You have probably heard of the normal (Gaussian) distribution, one of the most widely used probability models in engineering and natural sciences.
Analyzing the following figure, the widest range — corresponding to ±3σ (three sigmas) — covers about 99.74% of signal values. This region is considered the natural range of variations of the process.
In statistics, every process exhibits some degree of variability; that is, it operates within a band of values. If the process is stable, variation will remain within this band.
Applying this concept to machine vibration, a random acceleration signal tends to produce a normal distribution similar to the following:
Kurtosis and Skewness: What they tell us
Kurtosis and Skewness (also translated as distortion or asymmetry) are two important statistical parameters used to qualitatively describe the shape of a vibration signal.
In the context of vibration analysis, they quantify peaks or flattening (kurtosis) and the degree of symmetry around the mean value (skewness).
Kurtosis (Tail Heaviness / Impulsiveness)
The kurtosis of a vibration signal can be interpreted graphically by examining the signal’s value distribution, as shown in the following figure:
- A signal with a normal (random) distribution has kurtosis ≈ 3 (excess kurtosis ≈ 0).
- A higher kurtosis yields a more tapered shape, with values concentrated around the mean and heavier tails — indicative of rare, high-amplitude impulses.
- A lower kurtosis yields a flatter shape, with values spread across a wider range — typical of steadier conditions.
In short: kurtosis expresses impulsiveness and how similar most signal values are relative to rare peaks. Therefore, signals with many distinct impacts or spikes will exhibit higher kurtosis.
Let’s look at some examples:
New bearing: Due to the absence of defects, a random signal is expected, such as the waveform below. In this case, kurtosis ≈ 3.
Defect evolution: As bearing defects emerge and evolve, impact events modify the distribution, raising kurtosis. Below, the signal exhibits high kurtosis = 10.
From any waveform, you can extract kurtosis using acceleration, velocity, displacement, and envelope domains, which makes analysis richer and more fault-specific.
More applications of Kurtosis
Time comparisons are valuable for identifying defect evolution. In the example of a vibrating screen exciter with an inner race bearing defect (spectral envelope illustrated below):
When we examine time-domain kurtosis in acceleration for this monitoring point and focus on a high-frequency band (1000 Hz to 6400 Hz), the value increases significantly.
As the defect evolves, the waveform shows a growing presence of peaks:
Importantly, these waveform parameters do not replace spectral analysis; they are complementary.
The best vibration diagnostics combine time-domain features, spectral techniques, and envelope analysis to reach a robust conclusion.
Skewness (Signal Asymmetry / Directional Bias)
Another parameter for assessing asset health is skewness — the asymmetry of a distribution relative to its mean.
It can be interpreted graphically by observing the shape of the signal’s distribution:
Positive skewness: the waveform has more prominent positive values; the distribution’s right tail is longer.
Negative skewness: the waveform has more prominent negative values; the distribution’s left tail is longer.
Returning to the defective bearing example, if the signal were fully symmetric, skewness = 0.
However, the waveform is trending downward, toward the negative half of the graph.
This produces negative skewness (-0.69) and a left-shifted distribution curve.
Such asymmetry may arise from the defect’s location or the local load distribution:
Another failure detectable via skewness is rotor rubbing, often similar to looseness but with truncation in the waveform:
Because the rotating part contacts the stationary surface, the signal shows strong negative asymmetry, yielding skewness = -1.48, as indicated in the statistics table.
Thus, any waveform not symmetric around the zero-vibration point tends to produce marked skewness values.
Why combining Kurtosis and Skewness improves fault diagnosis
- Early sensitivity: Rising kurtosis frequently flags impulsive anomalies before RMS or temperature changes become obvious.
- Directional insight: Skewness clarifies whether extremes skew positive or negative, improving diagnostic confidence.
- Complementary evidence: Together, these metrics strengthen decisions, especially when envelope spectra and fault frequencies corroborate the trend.
- Asset management impact: Consequently, teams can plan interventions proactively, reduce risk, and align maintenance to business objectives.
Best practices and practical tips on Kurtosis and Skewness
Segment steady-state: Avoid non-stationary segments (startups, speed ramps) when computing kurtosis and skewness; otherwise, metrics can inflate.
Use band-pass + envelope: Isolate fault bands before calculating features to improve signal-to-fault sensitivity.
Compare domains: Examine acceleration, velocity, displacement, and envelope — different domains emphasize different fault characteristics.
Trend vs. baseline: Track metrics over time and compare to healthy baselines or peer assets; prefer relative thresholds (e.g., z-scores).
Validate with spectra: Always corroborate with spectral indicators (bearing BPFO/BPFI/BSF/FTF, gear mesh & sidebands).
Document context: Tag changes in load, speed, temperature, lubrication, and mounting to avoid misinterpretation.
Conclusion
Integrating Kurtosis and Skewness in Asset Management enhances defect detection, reveals directional bias, and enriches diagnostic decisions. Therefore, combining these distribution-based features with conventional metrics and spectral analysis leads to smarter maintenance, higher reliability, and lower total cost of ownership.
Ready to improve asset reliability? Discover how Dynamox solutions leverage Kurtosis and Skewness for smarter diagnostics. Request a Demo and see advanced signal analysis in action.
Frequently Asked Questions (FAQ)
What is the difference between Kurtosis and Skewness?
Kurtosis measures impulsiveness and the heaviness of distribution tails; Skewness measures asymmetry around the mean (positive vs. negative bias).
Are high kurtosis values always a sign of damage?
Not always. Transient knocks, installation changes, or process shocks can raise kurtosis. Always validate with spectra and operational context.
Should I compute features on raw or filtered signals?
Both add value; however, band-pass filtering and envelope detection target fault-related content and improve sensitivity to impacts.
How do load and speed changes affect these metrics?
Non-stationary operation can inflate both metrics. Segment data into steady-state windows or maintain separate baselines for each operating band.
Which domains should I monitor (acceleration, velocity, displacement, envelope)?
Monitor multiple domains. Acceleration and envelope are often more sensitive to impulsive faults; velocity may align better with human perception of vibration severity.
How do I set alert thresholds?
Use baseline-driven thresholds and z-scores (e.g., alert when kurtosis deviates by more than 3σ from baseline). Avoid one-size-fits-all static limits.
Do these metrics replace spectral analysis?
No. They are complementary. The strongest diagnosis combines time-domain features, spectral indicators, and process context.
Can skewness help differentiate failure modes?
Yes. Negative skewness may indicate directional rubbing or looseness; positive skewness often reflects impulsive positive peaks, such as early bearing defects.