Breviary Technical Ceramics






10.6.2 Statistical Methods Computation Magnitudes

If a random sample is taken in order to inspect a large number of parts, a finite number of measured values are obtained. If a sufficiently large number of measurements is taken, a continuous curve can be drawn representing the entirety of all parts, even those that were not measured.

The curves associated with distributions are distinguished by their position, width and shape; they can occur next to each other and can be superimposed. Data very often display a normal distribution, also called a Gaussian distribution or bell curve, due to its form.

The normal distribution is mathematically described by the two following variables.

Arithmetic mean:

where n = number of values with individual values Xi from X1 to Xn

Standard deviation:

The mean value, x, is the centre of the normal distribution curve and indicates the position of the distribution.
The standard deviation, s, describes the scattering of the process. It is a measure of the width of the normal distribution curve, and is the distance between the mean value, x, and the inflection point of the normal distribution.

The area under the normal distribution curves is proportional to the frequency with which the values occur. In the region within ± 1 s around the mean value x, i.e. 2 s, the hatched area underneath the normal distribution curve contains 68.26 % of all the values. The region ± 3 s around the average value, that is 6s wide, covers 99.73 % of all values. The points 3s from the mean value are defined as the natural process boundaries.


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