Unchanging concepts - Concrete Mix Design, Quality Control and Specification - page 262

11.3.3 Numerical cusum
The previous mean value is subtracted from each result and if the difference
numerically exceeds a selected margin, the difference (less the margin) is
accumulated in a register. If the accumulated total exceeds a selected limit,
a detection has occurred. In practice positive and negative registers are
maintained (because detection of an upturn means that cement can be
saved, which is a further reason to prefer numerical cusum) but for the cur-
rent exercise, only a negative register was maintained.
For any selected margin, a limit can be chosen to give whatever frequency
of false alarms is considered acceptable. It is conventional to choose a mar-
gin of about half the minimum change it is desired to detect. If this is
considered to be 0.5 × SD, then SD/4 might be the chosen margin. The
investigation reported started with a margin of SD/3 and a limit of 4 × SD,
but after comparative trials the best results were obtained with a margin of
SD/6 and a limit of 5.5 × SD.
The use of a numerical cusum in this way is exactly equivalent to using
a graphical V-mask technique (Devore) as is used in the United Kingdom.
11.3.4 Assessment of alternatives
On average and after adjustment to a comparable false alarm frequency, the
running mean of five gives the quickest detection. However the numerical
cusum follows close behind and is better at detecting very small drops.
Numerical cusum is also more directly aimed at detecting change from
a previous situation rather than infringement of a specified limit. Since a
producer would be ill-advised to work right down to the limit, the latter
is likely to be the more useful feature. Numerical cusum is also equally at
home in detecting upturns and this is important to the producer. Of course
a running mean of five can be adapted to all these purposes, but this is not
often done.
The national systems are not strictly comparable as they have different
intended methods of application. The American ACI 214 publication sets
out a range of possibilities together with several pages of excellent advice
and information with the objective of allowing specifiers to make their own
informed decisions. It also includes a recommendation to maintain control
charts and detailed advice on how to do so.
The British BS 5328 condenses its unequivocal requirements into a small
table and four carefully chosen sentences. To be fully comparable with the
ACI system it would also be necessary to make reference to the require-
ments of the British Quality Scheme for Ready Mixed Concrete, which
is an industry based self-regulatory body and recommends cusum control
charts or an alternative counting rule system involving not more than eight
consecutive results below the previous mean.