Page 103 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

90 • using ansys for finite eLement anaLysis

Weibull CDF (g = 0.5) Weibull CDF (g = 1)
0.8 1
0.6
Probability 0.4 Probability 0.5
0.2
0 0
0 1 2 3 4 5 0 1 2 3 4 5
x x
Weibull CDF (g = 2) Weibull CDF (g = 5)
1 1
Probability 0.5 Probability 0.5

0 0
0 1 2 3 4 5 0 1 2 3 4 5
x x
Figure 3.9. The Weibull cumulative distribution function for four values of g.

3.2.5.3 Common Statistics

 g +  1
Γ   g   ,

Mean ∞
t −
Γ a () = ∫ t a−1 edt
a
where Γ is the gamma function

Median ln 2 () 1 g
1
 1− 1 g g � > 1
Mode     g

0 g ≤ 1
Range Zero to positive infinity.

1
Standard Deviation Γ    g +  2  −    Γ    g +  2

g 
g 
 g +  2
Γ   g  
Coefficient of Variation 2 −1
  g + 
1

  Γ   g 