Rockwell-automation Arena Basic Edition Users Guide Manuale Utente Scaricare il pdf (Pagina 79)

A • STATISTICAL DISTRIBUTIONS

• • • • •

A • Statistical Distributions

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

+ m

+ 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)

am b

for a ≤ x ≤ m

for m ≤ x ≤ b

f(x) =

2 xa–()

ma–()ba–()

-----------------------------------

2 bx–()

bm–()ba–()

-----------------------------------

0otherwise

Parameters

Range

Mean

Variance

Applications

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Rockwell-automation Arena Basic Edition Users Guide Manuale Utente Pagina 79