Template:MedianRanks: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
(Replaced content with 'Category: For Deletion')
 
Line 1: Line 1:
==== Median Ranks  ====
[[Category: For Deletion]]
 
Median ranks are used to obtain an estimate of the unreliability for each failure. It is the value that the true probability of failure, <span class="texhtml">''Q''(''T''<sub>''j''</sub>),</span> should have at the <span class="texhtml">''j''<sup>''t''''h '''''</sup></span>failure out of a sample of ''N ''units at the 50% confidence level.
 
The rank can be found for any percentage point, <span class="texhtml">''P''</span>, greater than zero and less than one, by solving the cumulative binomial equation for <span class="texhtml">''Z''</span> . This represents the rank, or unreliability estimate, for the <span class="texhtml">''j''<sup>''t''''h'''''</sup></span> failure in the following equation for the cumulative binomial:
 
::<math>P=\underset{k=j}{\overset{N}{\mathop \sum }}\,\left( \begin{matrix}
  N  \\
  k  \\
\end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>
 
where <span class="texhtml">''N''</span> is the sample size and <span class="texhtml">''j''</span> the order number.
 
The median rank is obtained by solving this equation for <span class="texhtml">''Z''</span> at <span class="texhtml">''P'' = 0.50,</span>
 
::<math>0.50=\underset{k=j}{\overset{N}{\mathop \sum }}\,\left( \begin{matrix}
  N  \\
  k  \\
\end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>
 
<br>For example, if ''N=4'' and we have four failures, we would solve the median rank equation for the value of ''Z'' four times; once for each failure with ''j= 1, 2, 3'' and ''4''. This result can then be used as the unreliability estimate for each failure or the ''y'' plotting position. (See also the chapter&nbsp;[[The Weibull Distribution|The Weibull distribution]]&nbsp;for a step-by-step example of this method.) The solution of cumuative binomial equation for ''Z'' requires the use of numerical methods.

Latest revision as of 12:24, 20 July 2012

Retrieved from "https://www.reliawiki.com/index.php?title=Template:MedianRanks&oldid=26765"