Statistical analysis - Concrete Mix Design, Quality Control and Specification - page 226

for a short period. However the within-sample error can be established
providing that two (or more) specimens from the same sample of concrete
are tested at the same age. Day introduced a system by which the con-
crete supplier's own control testing was accepted as the project control
providing that he produced double sets of specimens at specified intervals
and delivered them to an independent laboratory for test. This is much
more economical than having an independent sampler on site and avoids
the concrete supplier claiming that the independent samples have been
incompetently sampled, cast, or field cured. The only remaining prob-
lem is that someone has to ensure that the selection of trucks for testing
is unbiased. This system is highly recommended wherever there is any
concern about the veracity of the supplier's own testing. However, the
net result is often that the supplier's testing is seen to be acceptable and
comparative testing discontinued.
It has been pointed out that even five specimens would not permit a
meaningful direct determination of standard deviation for a single sample.
However, another piece of statistical theory shows that the average differ-
ence between many pairs of specimens from different samples is related to
the within-sample standard deviation by the simple equation
Within sample standard deviation = Average pair difference/1.13
(In the case of sets of three specimens the difference between highest and
lowest, that is, the range, may be used in the same way, and in this case the
1.13 becomes 1.69.)
Generally there is no point in converting to standard deviation for
our purposes and the average pair difference is directly monitored. The
best achievable average pair difference on normal concrete is 0.5 MPa
(say 75 psi) and between 0.5 and 1.0 MPa can be considered acceptable.
However, the authors have encountered reputable laboratories with a pair
difference consistently in excess of 1.5 MPa. The seriousness of this situ-
ation can be appreciated when it is realised that even this figure does not
include sampling error and that a really top class producer can work to an
overall standard deviation of concrete quality below 2.0 MPa. As discussed
earlier we must not fall into the error of saying that testing is three quarters
of the total variability (and remember the 1.13 factor) but nevertheless such
testing is grossly unfair to the producer.
9.6 COEFFICIENT OF VARIATION
Another measure of variability is the coefficient of variation. This is
the standard deviation divided by the mean strength and expressed as a
percentage. The question is which of the two parameters best measures