Civil Engineering Reference
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f
c
-1.72σ
1.28
(σ
1
- σ
2
)
f
c
(
k
= 1.28)
f
+1.28σ
2
(σ
2
= 2.5)
f
+1.28σ
1
(σ
1
= 5.0)
(3σ
2
- σ
2
)
f
c
- 5
(
k
= 3)
f
c
- 5
+3σ
2
(σ
2
= 2.5)
f
c
- 5
+3σ
1
(σ
1
= 5.0)
Figure 11.2
Effect of compensated increase in
k
is to improve competitive position of
low-variability supplier and rule out low results from high-variability supplier.
but could be applied with mutual agreement in practice. The effect of ana-
lysing 30 results overlapping a change point is to give an artificially inflated
standard deviation, which is only slightly compensated for by the increased
mean strength obtained from the inclusion of a few higher results and,
therefore, causes a higher penalty. An alternative, slightly lower penalty
based on the actual defective period can be offered, but the specification
can be strictly enforced without substantial unfairness.
Figure 11.3 shows a run of understrength results that merit a penalty.
Under the proposed specification, the lowest 30-result section (representing
600 m
3
[785 yd
3
] of concrete) must form the basis.
1
A penalty of $6.16 m
3
would be applied, totaling $3696.
Close analysis, however, reveals that the low strength concrete is con-
fined to a 20-result section (representing 400 m
3
[523 yd
3
] of concrete).
2
The penalty/m
3
based on the 20 results would be greater but the overall
penalty would be less at $7.67 × 400 = $3068. The latter penalty is the
more equitable and is the one that should actually be imposed. However,
1
The average strength over the thirty results in 31.56 MPa (or 2.28 MPa less than the target
of 33.84 MPa based on a SD of 3 MPa and K = 1.28).
2
The average strength over the twenty results is 31 MPa (or 2.84 MPa less than the target).
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