ALTA ALTA Standard Folio Data Eyring-Lognormal: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
← Older editNewer edit →
Nicolette Young (talk | contribs)
Poweruser
11,985 edits
No edit summary
No edit summary
Line 8: Line 8:
|  valign="middle" |{{Font|Standard Folio Data Eyring-Lognormal|11|tahoma|bold|gray}}
|  valign="middle" |{{Font|Standard Folio Data Eyring-Lognormal|11|tahoma|bold|gray}}
|-
|-
|  valign="middle" | {{Font|ALTA|10|tahoma|bold|gray}}
|  valign="middle" |
Content 1
|}
<br>
{{Font|Learn more from...|11|tahoma|bold|gray}}
{| border="0" align="left" cellpadding="0" cellspacing="3"
|-
|-
|  valign="middle" |
| [[Image:Helpblue.png]]
The  <math>pdf</math> of the lognormal distribution is given by:
| [http://help.synthesis8.com/weibull_alta8/alta_standard_folios.htm the help files...]
|-
| [[Image:Book blue.png]]
| [http://reliawiki.com/index.php/Template:Erying-log#Eyring-Lognormal the theory textbook...]  
|-
| [[Image:Articleblue.png]]
| [http://www.weibull.com/hotwire/issue74/relbasics74.htm related article(s)...]
|-
| [[Image:Bulbblue.png]]
| [http://reliawiki.com/index.php/Template:Example:Eyring#Eyring_Example use example(s)...]
|}
 
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
<math>f(T)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'-\overline{{{T}'}}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
<br>
<br>
where:
<br>
<br>
<math>{T}'=\ln (T)</math>
<br>
<br>
<math>T=\text{times-to-failure}</math>
<br>
<br>
and:
<br>
<br>
• <math>\overline{{{T}'}}=</math> mean of the natural logarithms of the times-to-failure.
• <math>{{\sigma }_{{{T}'}}}=</math> standard deviation of the natural logarithms of the times-to-failure.
<br>
<br>
The Eyring-lognormal model can be obtained first by setting  <math>\breve{T}=L(V)</math> in Eqn. (eyring). Therefore:
<br>
<br>
<math>\breve{T}=L(V)=\frac{1}{V}{{e}^{-(A-\tfrac{B}{V})}}</math>
<br>
<br>
or:
<br>
<br>
<br>
<br>
<math>{{e}^{{{\overline{T}}^{\prime }}}}=\frac{1}{V}{{e}^{-(A-\tfrac{B}{V})}}</math>
<br>
<br>
Thus:
<br>
<br>
<br>
<br>
<math>{{\overline{T}}^{\prime }}=-\ln (V)-A+\frac{B}{V}</math>
<br>
<br>
Substituting Eqn. (eyr-logn-mean) into Eqn. (Eyr-logn-pdf) yields the Eyring-lognormal model  <math>pdf</math> 
or:
<math>f(T,V)=\frac{1}{T\text{ }{{\sigma }_{{{T}'}}}\sqrt{2\pi }}{{e}^{-\tfrac{1}{2}{{\left( \tfrac{{T}'+\ln (V)+A-\tfrac{B}{V}}{{{\sigma }_{{{T}'}}}} \right)}^{2}}}}</math>
|-
| valign="middle" | [http://reliawiki.com/index.php/Template:Erying-log#Eyring-Lognormal Get More Details...]
|-
| valign="middle" | [http://reliawiki.com/index.php/Template:Example:Eyring#Eyring_Example See an example]
|}
<br>




[[File:docedit.png|20px|right|link=http://www.reliawiki.com/index.php?title=ALTA_ALTA_Standard_Folio_Data_Eyring-Lognormal&action=edit]]
[[File:docedit.png|20px|right|link=http://www.reliawiki.com/index.php?title=ALTA_ALTA_Standard_Folio_Data_Eyring-Lognormal&action=edit]]

Revision as of 17:14, 7 March 2012

Standard Folio Data Eyring-Lognormal

Content 1


Learn more from...

the help files...
the theory textbook...
related article(s)...
use example(s)...

























Retrieved from "https://www.reliawiki.com/index.php?title=ALTA_ALTA_Standard_Folio_Data_Eyring-Lognormal&oldid=19501"