Statistical analysis - Concrete Mix Design, Quality Control and Specification - page 216

indicating what caused it. Thus if a single low test result is from the lighter
of a pair of specimens, it can be neglected, but if a low pair of strengths are
accompanied by a high slump reading they must be accepted as fact but still
may not indicate a need for a mix revision, only for better slump control.
Some crude statistical techniques have been used by the authors. This
has been done quite deliberately since, in our opinion, more mathematical
sophistication would not help. Rather, what is needed by way of sophistica-
tion is a very thorough realisation of what factors may cause conclusions
to be unrealistic, how unrealistic they might be and what can be done to
ensure that such conclusions are weeded out and do not lead to inappropri-
ate control action. The total amount of sophistication in a scheme must be
limited to keep it within the capability of ordinary practitioners. It must
always be borne in mind that the objective is to achieve more economical
operation rather than to display virtuosity.
9.1 NORMAL DISTRIBUTION
If a mathematical description or pattern of a set of results can be found,
it may be possible to establish what the pattern is from a limited number
of results already obtained and use it to predict what future results will be
obtained if the current pattern continues to apply. For example, it may be
possible without ever having obtained a result below some particular value
to predict that a result below that value will inevitably occur unless action
is taken to change the pattern. We shall be in a much stronger position to
control concrete quality if it can be established that control action is neces-
sary without experiencing even one “failure” than if we have to wait for
failures before reacting to them. The position will be even stronger if it can
be established from early-age tests or even from tests on the freshly supplied
concrete, rather than from 28-day results.
If each result is considered as a ball and a number of slots corresponding
to strength ranges are set up (e.g., 22.5 to 25 MPa, 25 to 27.5 MPa, 27.5 to
30 MPa) each result can be placed in its slot giving a picture like Figure 9.1.
Such a figure is known as a histogram. If we have a very large number of
balls and divide them into narrower slots, the result may approximate to
the typical smooth distribution curve.
One purpose of introducing Figure 9.1 was to make it clear that area
under the normal distribution curve represents number of results. Just as
each ball occupies the same area in the two-dimensional representation, so
each unit of area in the normal distribution represents a fixed proportion
of test results. This type of graphical representation is called a frequency
distribution or just a distribution. There are many different shapes of dis-
tribution curves known to statisticians but the particular bell shaped curve
shown is called a normal distribution. It can be constructed from a standard