## Statistics

Most measurements are influenced by random factors. A single value cannot describe the true quantitative property of a measured entity. For that, repeated measurements and multiple individual values are necessary. And statistical methods are required to evaluate the repeated measurements.

From a sufficiently large number of measured values, one can identify the mean value and the corresponding variance. Then it is possible to calculate the distribution of the individual values around the mean value. Often, the distribution produces a Gaussian bell curve – a curve that applies to many technical processes; it shows the probability distribution based on the measured values.

However, in most coating processes, one finds an asymmetric distribution. This "log-normal distribution" is typical for measured variables that can only have positive values, like those found in many growth processes in nature, or the thickness of a coating.

Using statistical distribution, it is possible to predict the thickness of the coating throughout the entire process – meaning that the process can be assessed without having to do 100% monitoring.

For our customers, the FISCHER instruments take over doing the statistical calculations. At the touch of a button, our instruments can turn the recorded measurement values into a variety of statistical reports.

https://en.wikipedia.org/wiki/Normal_distribution
https://en.wikipedia.org/wiki/Log-normal_distribution 