Anomaly Detection for Monitoring

(say, the size of the drill bit), and the control lines are fixed some
number of standard deviations away from that mean. If you’ve heard
of the three sigma rule, this is what it’s about. Three sigmas represents
three standard deviations away from the mean. The two control
lines surrounding the mean represent an acceptable range of
values.
The Gaussian (Normal) Distribution
A distribution represents how frequently each possible value occurs.
Histograms are often used to visualize distributions. The Gaussian
distribution, also called the normal distribution or “bell curve,” is a
commonly used distribution in statistics that is also ubiquitous in
the natural world. Many natural phenomena such as coin flips,
human characteristics such as height, and astronomical observations
have been shown to be at least approximately normally distributed.
3 The Gaussian distribution has many nice mathematical
properties, is well understood, and is the basis for lots of statistical
methods.
Figure 3-1. Histogram of the Gaussian distribution with mean 0 and
standard deviation 1.
One of the assumptions made by the basic, fixed control chart is that
values are stable: the mean and spread of values is constant. As a
formula, this set of assumptions can be expressed as: y = μ + ɛ. The
3 History of the Normal Distribution
Statistical Process Control | 17