Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 131

“variables,” even though a single value of the variable, such as the average, may be used in
calculations.
While the average value of a variable is useful, and sufficient for many purposes, other
characteristics of scattered measured values are also important, and are needed for calcula-
tions that reflect the level of uncertainty in the measured values. The standard deviation
and the coefficient of variation (COV), defined below, are useful measures of the degree of
scatter in a set of values of a variable.

3.3.2 Correlated and uncorrelated variables
The reliability methods as presented in this chapter (Taylor Series, Point Estimate, Simplified
Hasofer Lind, and Monte Carlo simulation) consider only “uncorrelated” variables, for two
reasons:

1. Determining correlation coefficients for geotechnical parameters is difficult and uncer-
tain, and

2. Incorporating correlation coefficients complicates reliability analyses.

Methods for incorporating correlation coefficients into reliability analyses can be found
in Baecher and Christian (2003), Harr (1987), Low (1996), Low and Tang (1997, 2004), and
Low and Phoon (2002).

3.3.3 Standard deviation
Standard deviation is a measure of dispersion, or scatter, in values of a variable.
The standard deviation (σ) is defined mathematically as the square root of the average of
the squared values of the difference between each of the measured values and the average,
as expressed in

n

∑ (

xx − )

2

i

i 1

σ= (3.1)

n − 1

where
σ is the “sample standard deviation” of n measured values of x
∑ =

1 is thesum of valuesfrom1to
x i is the i th measured value
x is the average of themeasured values
n is the number of values

n

n

i

A slightly different standard deviation is the “population standard deviation” which is
calculated using Equation 3.2

n

∑ (

xx
n

− )

2

i

i = 1

σ= (3.2)