Statistical analysis - Concrete Mix Design, Quality Control and Specification - page 222

Looked at in this way, the American choice of 1.28 is seen to provide less
incentive to achieve low variability than the more usual 1.64 or 1.65, and
the authors would prefer to use a value of 2 or even 3. The reduced incen-
tive may explain a reduced interest and attainment in the United States in
matters of QC.
Having discounted the realism or otherwise of the theoretical percentage
defective as a basis for choosing the value of k , there is another consideration.
This is the accuracy with which σ can be assessed. Section 9.4 provides
details.
Taking the data from Tables 9.2 and 9.3 together, it is seen that the error
of estimation of the mean of three results is about five times the error in
estimating the standard deviation from the last 30 results and almost four
times that from 20 results. A proposal to multiply the standard deviation by
2 or 3 would therefore be reasonable if the σ were based on at least the last
30 results. However, it should be realised that a standard deviation change
of less than ±25% from its previous value would not be significant.
There is a further consideration in increasing the number of results on
which the standard deviation is based. If the results analysed extend across
a change point in mean strength, the standard deviation will be artificially
inflated. Care is necessary in determining the desired result. As discussed in
Chapter 8, the variability between change points is the basic variability of

Table 9.2 Error in mean for various values of standard deviation
Standard deviation (SD) values

2 3 4

Number of results
1

3.30 4.95 6.60

2 2.33 3.49 4.65

3 1.91 2.86 3.81

5 1.47 2.21 2.95

10 1.04 1.56 2.08

20 0.73 1.10 1.46

30 0.60 0.90 1.20

Table 9.3 Error in standard deviation for various values of true
standard deviati on
Standard deviation values 2 3 4

Number of results
2 1.65 2.48 3.30

5 1.05 1.58 2.09

10 0.74 1.11 1.48

30 0.42 0.63 0.85