Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 149

If the only method of determining values of standard deviation was to use Equation 3.12 ,
reliability analyses could not be used much in geotechnical engineering, because in many
cases the values of some parameters are estimated using correlations or experience, and
there is no real “data” that can be used with Equation 3.12 . In order to be able to apply
reliability analyses to these common situations, it is necessary to estimate values of stan-
dard deviation, rather than to calculate them. Three methods of estimating values of σ are
described in the following sections.

3.5.2 Published values
When correlations or experience is used to estimate parameter values, correlations or expe-
rience can also be used to estimate standard deviations. It is convenient in these cases to use
the COV:

Standard deviation
Average value

σ
x

COV = = (3.13)

from which the standard deviation can be computed:

()

σ= ( COV ) x (3.14)

Values of COV for a number of geotechnical engineering parameters and in situ tests,
compiled by Harr (1984), Kulhawy (1992), Lacasse and Nadim (1997), and the authors of
this chapter are listed in Table 3.6. The best aspect of the values in Table 3.6 is that they
are based on a large number of tests. However, the conditions of sampling and testing,
which have a great influence on the variability of the test results, are not available for the
data shown in Table 3.6 , and the values therefore provide only a rough guide for estimating
values of COV for any particular case. It is important to use judgment in applying values of
COV from published sources, and to consider as well as possible the likely degree of uncer-
tainty in the particular case at hand.

3.5.3 the “three-sigma rule”
Dai and Wang (1992) suggested that values of standard deviation could be estimated using
what they called the “three-sigma rule.” This rule uses the fact that 99.73% of all values of
a normally distributed parameter fall within plus or minus three standard deviations (three
sigma) from the average. Thus, an extreme low value would be three standard deviations
below the average, and an extreme high value would be three standard deviations above the
average. They suggested that, by estimating the extreme high and low values, and divid-
ing the difference between them by six, the standard deviation could be estimated using
Equation 3.15 :

HCV CV
6

−

σ= (3.15)

where HCV is the highest conceivable value and LCV the lowest conceivable value.
The three-sigma rule has the advantage that it can be used to estimate values of standard
deviation for parameters whose values are estimated based entirely on judgment, or on judg-
ment plus meager data.