Kurtosis is a statistical parameter that essentially measures how “peaky” a signal is.
It is expressed as a “K” number. A random signal would have a kurtosis of 3, or K = 3, and a serious defect would have K over 20.
The higher the kurtosis number, the more significant amplitude peaks there are.
Kurtosis has a complicated definitions, but in simple terms, it measures how “similar” all the values are. For example, if the signal is noise, then all of the values are similar and the kurtosis number is low.
If the signal has one large peak plus noise, the kurtosis value will not change, but the crest factor will change a great deal. But the kurtosis value will increase if there are a lot of spikes.
Peak, as a measurement, will include a single large peak, but kurtosis only looks at multiple peaks. The signals below have the same crest factor, but the kurtosis differs greatly. This is because the top time waveform has many more high-amplitude peaks than the bottom waveform.
In the signal below, the green shows a kurtosis of 3 and the purple shows a kurtosis of 4. There are more purple spikes sticking out from the base RMS.