Template:Logistic reliability function: Difference between revisions

Revision as of 23:01, 14 February 2012

The reliability for a mission of time [math]\displaystyle{ t }[/math] , starting at age 0, for the logistic distribution is determined by:

[math]\displaystyle{ R(t)=\int_{t}^{\infty }f(t)dt }[/math]

or:

[math]\displaystyle{ R(t)=\frac{1}{1+{{e}^{z}}} }[/math]

The unreliability function is:

[math]\displaystyle{ F=\frac{{{e}^{z}}}{1+{{e}^{z}}} }[/math]

where:

[math]\displaystyle{ z=\frac{t-\mu }{\sigma } }[/math]

@@ Line 1: / Line 1: @@
 ==The Logistic Reliability Function==
-The reliability for a mission of time  <math>T</math> , starting at age 0, for the logistic distribution is determined by:
+The reliability for a mission of time  <math>t</math> , starting at age 0, for the logistic distribution is determined by:
-::<math>R(T)=\int_{T}^{\infty }f(t)dt</math>
+::<math>R(t)=\int_{t}^{\infty }f(t)dt</math>
-:or:
+or:
-::<math>R(T)=\frac{1}{1+{{e}^{z}}}</math>
+::<math>R(t)=\frac{1}{1+{{e}^{z}}}</math>
 The unreliability function is:
@@ Line 12: / Line 12: @@
 ::<math>F=\frac{{{e}^{z}}}{1+{{e}^{z}}}</math>
-:where:
+where:
-::<math>z=\frac{T-\mu }{\sigma }</math>
+::<math>z=\frac{t-\mu }{\sigma }</math>