Statistical analysis - Concrete Mix Design, Quality Control and Specification - page 225

excellent paper on concrete quality control (Graham and Martin, 1946).
The square of the standard deviation is called the variance. Standard devia-
tions are not additive, but variances are. This can be illustrated using the
famous example in question (the standard deviations are in psi).

Source of error Standard deviation (psi)

Cement (C) 240

Batching (B) 462

Testing (T) 188

The overall error is not given by C + B + T = 890 but by √(C 2 + B 2 + T 2 ) = 553.
The effect of this situation is that the contribution of all but the largest com-
ponent of overall variability is reduced. Thus totally eliminating cement
variability would give an overall variability of √ (B 2 + T 2 ) = 499, a reduc-
tion of only approximately 10%. But in the famous paper, the variability
of the cement was further exaggerated by including the error in testing the
cement and it was reported that cement variability accounted for 48.2% of
total variability. This was a very significant error because it suggested that
much of the variability was outside the concrete producer's control. Thus
one would be led to putting much of the control effort into cement test-
ing, instead of where it was most needed (slump control). This is a lesson
that must be learned if economical control is to be achieved. The primary
(largest) cause of variability must be found and control action concentrated
on it (see also Pareto's principle, Chapter 10).
Of course it is necessary to monitor subsidiary causes as well to estab-
lish which is the major cause (and to check that what was initially the
major cause has not been overtaken by some other cause); however the real
control effort must be correctly directed.

9.5 TESTING ERROR

It has been argued elsewhere (Chapter 11) that testing itself is a signifi-
cant source of error on a typical project and that it must be monitored.
Day (1981) has experienced two different testing organisations testing the
same truck of concrete and getting results differing by as much as 10 MPa
(1450 psi) on occasions and as much as 3 MPa (435 psi) on average over a
substantial number of samples (Day, 1981).
The error in question covers all aspects of taking a representative
sample and casting, curing, capping, and testing specimens. It is only
possible to fully establish the magnitude of this error by taking two
samples from the same truck, and this is rarely economically practi-
cable unless serious malpractice is suspected and is to be investigated