Statistical analysis - Concrete Mix Design, Quality Control and Specification - page 224

This is a generally applicable statement and is another reason for preferring
low variability concrete.
It will be seen that if a single test result is obtained to represent a truck of
concrete, or even the mean of a pair, the assessment will not necessarily be
very precise, particularly if we are dealing with variable concrete. However,
variation within a batch, that is, within a single truckload, is a different
matter to variability between batches and is largely a matter of testing error
rather than variability of concrete (see Chapter 7). Likewise if a day's sup-
ply of concrete is assessed on the basis of three samples of concrete, a con-
siderable error may be involved.
9.3 VARIABILITY OF STANDARD
DEVIATION ASSESSMENT
In a similar manner, the value of the standard deviation (σ) obtained from
analysing a limited number of results will differ from the true value for all
the concrete. In this case the standard deviation of the distribution of stan-
dard deviations (no, it isn't a misprint!) is given by SD where
SD = σ/ √ 2 n
A table (Table 9.3) similar to Table 9.2 can be constructed. Although
these errors are a little smaller than those in the case of the mean, they are
a very much larger percentage error. Note that a group of 5 will only yield
a σ value to approximately ±50% accuracy. What this means is that the
variability of a group of less than 10 results simply cannot be determined
with reasonable accuracy.
This has had a profound influence on the basis of specifications, because
if we persist in trying to judge the quality of concrete on the basis of a small
number of samples, it is not possible to give any credit for low variability
(unless this is assessed on a basis external to the group of results in question).
Even the inaccuracy in the mean value noted previously is large enough to
require a large tolerance if good concrete is not to be rejected and this toler-
ance results in excessive leniency for poor concrete (see Figure 9.4a). However
there is no objection to framing a criterion involving the mean of the last 3,
4, or 5 results and the standard deviation of the last 10, 20, or 30 results.
9.4 COMPONENTS OF VARIABILITY
One further piece of statistical theory is needed. This is how variabilities
due to separate causes combine to give an overall variability. There is
a famous example of a wrong assumption about this marring an otherwise