Median Ranks: Difference between revisions

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Median ranks are used to obtain an estimate of the unreliability, <math>Q({{T}_{j}}),</math> for each failure at a <math>50%</math> confidence level. In the case of grouped data, the ranks are estimated for each group of failures, instead of each failure.
#REDIRECT [[Parameter_Estimation#Median_Ranks]]
For example, when using a group of 10 failures at 100 hours, 10 at 200 hours and 10 at 300 hours, Weibull++ estimates the median ranks (<math>Z</math> values) by solving the cumulative binomial equation with the appropriate values for order number and total number of test units.
For 10 failures at 100 hours, the median rank, <math>Z,</math> is estimated by using:
 
::<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>
 
 
with:
 
::<math>N=30,\text{ }J=10</math>
 
 
where one <math>Z</math> is obtained for the group, to represent the probability of 10 failures occurring out of 30.
For 10 failures at 200 hours, <math>Z</math> is estimated by using:
 
::<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>
 
 
where:
 
::<math>N=30,\text{ }J=20</math>
 
 
to represent the probability of 20 failures out of 30.
For 10 failures at 300 hours, <math>Z</math> is estimated by using:
 
::<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>
 
 
where:
 
::<math>N=30,\text{ }J=30</math>
 
 
to represent the probability of 30 failures out of 30.

Latest revision as of 22:50, 21 August 2012

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