Concepts of Error Analysis

a. Measurements of any nature have errors associated with them, causing
some  degree  of  uncertainty  in  the  resulting  data.
Unfortunately,  the
usefulness  of  a  measurement  is  dependent  upon  the  accuracy  of  that
measurement  or  its  closeness  to  the  true  value,  which  necessarily  is
The  purpose of  an error  analysis  is to  estimate  the  bounds
(reasonable limits) of the inaccuracies of the measurement at some arbitrary
level of confidence.
Basic to any error analysis is the idea that a
measurement is the result of data-taking (known as the measurement process).
This  process  inevitably  generates  errors,  resulting  in  an  inexact
You should analyze the process by which the measurement was
b. This  inexactness,  or  uncertainty  of  the  measurement  process
typically has two components: systematic error and random error.  (Another
type of error that will be addressed later in this lesson is the gross
error, or the error created by the operator.)  Systematic error usually can
only be estimated and does not follow the laws of probability.
It is
similar to misalined sights on a rifle where any shot group, no matter how
tight, would be off the bull's eye by the amount of this systematic error.
The systematic error in this case, however, is measurable in both magnitude
and direction upon looking at the target.
With a true systematic error,
neither of these attributes is known.  If the magnitude and direction of the
systematic error can be determined, it becomes a correction and is then no
longer  a  systematic  error.
In  calibration  systems  there  are  usually
systematic errors that cannot be measured in magnitude or in direction.
Random error, in contrast, follows the  laws of probability and can be
analyzed  by  statistical  methods.
In  the  above  example,  random  error
(impression) is similar to the dispersion of the shot pattern.  Figure 1 is
a pattern of five shots on a target by a rifle with misalined sights.
Distance A would be a systematic error in the shooting process, if there
were no target to show the magnitude (2 inches) and the direction 5.0 from
the vertical of the misalinement.
The circle B is an indication of the
random error of the process - in this case it encloses 100% of a very small
sample of shots.
Figure 1.
Shot pattern


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