Biomedical Engineering Reference
In-Depth Information
and “error” are often used interchangeably, they in fact have some-
what different meanings (ISO, 1995). When one makes a measure-
ment, one virtually always makes an error. That error is unknowable.
What one can do is to evaluate in some way the magnitude of
the error one is likely to have made and express this as an uncertainty
in the measured value. That is, uncertainty expresses the chance that
an error of at least a given magnitude has been made. One can have a
large uncertainty while having made, in fact, only a very small error.
R
ANDOM AND
S
YSTEMATIC
E
RRORS
When one makes repeated measurements, for example with a ruler of
the size of some object, and plots the frequency distribution of the
measurements, the result is likely to closely approximate a Gaussian
(often termed “normal”) distribution - an example of which is shown
in Figure 2.2, below. These variations in the results of the measure-
ments are due to
random error
. On the other hand, if the ruler's scale
is erroneously calibrated, then, even if the extent of the random errors
is negligible, one will consistently and unknowingly make the same
error. This is a
systematic error
. Finally, if the observer simply makes
a mistake, such as adding a digit to the recorded measurement, he or
she has made a
blunder
. The consequences of blunders are usually
omitted from uncertainty estimates. The likelihood of many types of
blunder can be greatly reduced by double-checking.
It has been traditional to describe the uncertainty associated with these
types of errors as random and systematic uncertainties However,
.
it is now recommended (ISO, 1995) that one refer to type A and type
B uncertainties. Rather than focus on the nature of the error, since
error is unknowable, the type A and type B designations refer to the
way the uncertainty was evaluated. If it was assessed by a “statisti-
cal analysis of a series of observations” (e.g., the distribution of the
results), then it is termed type A. If by other means, then it is said to
be of type B.
In radiation therapy, both random and systematic errors occur.
However, as an inspection of the list at the beginning of this chapter
will readily suggest, probably the majority of significant errors in
radiation therapy are systematic in nature, at least insofar as their
repetition throughout a treatment of many fractions is concerned.
