Rockwell Automation Arena Users Guide User Manual
Page 133
A
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TATISTICAL
D
ISTRIBUTIONS
125
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Stati
stica
l Di
str
ibution
s
Triangular(a, m, b)TRIANGULAR(Min, Mode, Max) or TRIA(Min,
Mode, Max)
The minimum (a), mode (m), and maximum (b) values for the distribution specified as
real numbers with a < m < b.
[a, b]
(a + m + b)/3
(a
2
+ m
2
+ b
2 –
ma – ab – mb)/18
The triangular distribution is commonly used in situations in which the exact form of the
distribution is not known, but estimates (or guesses) for the minimum, maximum, and
most likely values are available. The triangular distribution is easier to use and explain
than other distributions that may be used in this situation (e.g., the beta distribution).
Probability
Density
Function
f(x)
0
a
m
b
x
for a
≤ x ≤ m
for m
≤ x ≤ b
f(x) =
2 x a
–
(
)
m a
–
(
) b a
–
(
)
-----------------------------------
2 b x
–
(
)
b m
–
(
) b a
–
(
)
-----------------------------------
0
otherwise
Parameters
Range
Mean
Variance
Applications