E1C04 09/14/2010
14:7:40 Page 123
Table 4.2
Standard Statistical Distributions and Relations Common to Measurements
Distribution
Applications
Density Function
Shape
Normal
Most physical properties that are
continuous or regular in time or
space with variations due to
random error
p x
ð Þ ¼
1
s 2p
ð Þ
1=2
exp
À
1
2
x À x
0
À
Á 2
s 2
"
#
p(x)
x'
Log normal
Failure or durability projections;
events whose outcomes tend to be
skewed toward the extremity of
the distribution
p x
ð Þ ¼
1
ps 2p
ð Þ
1=2
exp
À
1
2
ln
x À x
0
À
Á 2
s 2
"
#
p(x)
Rectangular
Processes in which a likely
outcome falls in the range
between minimum value
a and
maximum value
b occurring with
equal probability
pðxÞ ¼
1
b À a
where
a x b, otherwise
pðxÞ ¼ 0
a
b
p(x)
Triangular
Process in which the likely
outcome
x falls between known
lower bound
a and upper bound
b,
with a peak value or mode
c; used
when population information is
sparse
pðxÞ ¼
2ðx
À aÞ
ðb À aÞðc À aÞ
for
a x c
¼
2ðb
À xÞ
ðb À aÞðb À cÞ
for
c < x b
a
c
d
p(x)
(Continued)
123