1.3. EDA Techniques
1.3.6. Probability Distributions
1.3.6.6. Gallery of Distributions
1.3.6.6.10. |
Fatigue Life Distribution |
The general formula for the probability density function of the fatigue life distribution is
where 
is the
shape parameter,
is the
location parameter,
is the
scale parameter,
is the probability density function
of the standard normal distribution, and
is the cumulative distribution
function of the standard normal distribution.
The case where = 0 and
= 1 is called the
standard fatigue life distribution. The equation for the
standard fatigue life distribution reduces to
Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function.
The following is the plot of the fatigue life probability density function.
where is the cumulative distribution
function of the standard normal distribution.
The following is the plot of the fatigue life cumulative distribution
function with the same values of
as the pdf plots above.
![G(p) = (1/4)*[gamma*PHI**(-1)(p) + SQRT(4+(gamma*PHI**(-1)(p))**2)]**2](eqns/flppf.gif)
where 
is the percent point
function of the standard normal
distribution. The following is the plot of the fatigue life percent
point function with the same values of
as the pdf plots above.
The following is the plot of the fatigue life hazard function with the
same values of as the pdf plots
above.
The following is the plot of the fatigue cumulative hazard function
with the same values of as the
pdf plots above.
The following is the plot of the fatigue survival function
with the same values of
as the pdf plots above.
The following is the plot of the gamma inverse survival function
with the same values of as
the pdf plots above.
| Mean |
|
| Range | Zero to positive infinity. |
| Standard Deviation |
|
| Coefficient of Variation |
|
