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| This example uses time-to-failure data from a life test done on incandescent light bulbs. The observed times-to-failure are given in the next table.
| | [[Category: For Deletion]] |
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| {| border="1" cellspacing="1" cellpadding="4" width="300" align="center"
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| |+ Observed times-to-failure for ten bulbs in hours.
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| |-
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| ! valign="middle" scope="col" align="center" | Order Number
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| ! valign="middle" scope="col" align="center" | Hours-to-failure
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| |-
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| | valign="middle" align="center" | 1
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| | valign="middle" align="center" | 361
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| |-
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| | valign="middle" align="center" | 2
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| | valign="middle" align="center" | 680
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| |-
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| | valign="middle" align="center" | 3
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| | valign="middle" align="center" | 721
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| |-
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| | valign="middle" align="center" | 4
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| | valign="middle" align="center" | 905
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| |-
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| | valign="middle" align="center" | 5
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| | valign="middle" align="center" | 1010
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| |-
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| | valign="middle" align="center" | 6
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| | valign="middle" align="center" | 1090
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| |-
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| | valign="middle" align="center" | 7
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| | valign="middle" align="center" | 1157
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| |-
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| | valign="middle" align="center" | 8
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| | valign="middle" align="center" | 1330
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| |-
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| | valign="middle" align="center" | 9
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| | valign="middle" align="center" | 1400
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| |-
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| | valign="middle" align="center" | 10
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| | valign="middle" align="center" | 1695
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| |}
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| '''Do the following:'''
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| #Plot the data on a Weibull probability plot and obtain the Weibull model parameters.
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| #Compute the B10 life of the bulbs.
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| Median ranks are used to obtain an estimate of the unreliability, <math>Q({T_j})</math> for each failure. It is the value that the true probability of failure, <math>Q({{T}_{j}}),</math> should have at the <math>{{j}^{th}}</math> failure out of a sample of <math>N</math> units at a <math>50%</math> confidence level. This essentially means that this is our best estimate for the unreliability. Half of the time the true value will be greater than the 50% confidence estimate, the other half of the time the true value will be less than the estimate. This estimate is based on a solution of the binomial equation. The rank can be found for any percentage point, <math>P</math>, greater than zero and less than one, by solving the cumulative binomial equation for <math>Z</math> . This represents the rank, or unreliability estimate, for the <math>{{j}^{th}}</math> failure[15; 16] in the following equation for the cumulative binomial:
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| <math>P=\underset{k=j}{\overset{N}{\mathop \sum }}\,\left( \begin{matrix}
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| N \\
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| k \\
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| \end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>
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| <br>where <math>N</math> is the sample size and <math>j</math> the order number. The median rank is obtained by solving this equation for <math>Z</math> at <math>P=0.50,</math>
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| <math>0.50=\underset{k=j}{\overset{N}{\mathop \sum }}\,\left( \begin{matrix}
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| N \\
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| k \\
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| \end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>
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| [[Category:Weibull_Examples]] | |