|
|
| Line 1: |
Line 1: |
| {{Banner Weibull Examples}}
| | [[Category: For Deletion]] |
| <noinclude>[[Category:NTI]]{{Template:InProgress}}</noinclude>
| |
| | |
| 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.
| |
| | |
| {| border="1" cellspacing="1" cellpadding="4" width="300" align="center"
| |
| |+ Observed times-to-failure for ten bulbs in hours.
| |
| |-
| |
| ! valign="middle" scope="col" align="center" | Order Number
| |
| ! valign="middle" scope="col" align="center" | Hours-to-failure
| |
| |-
| |
| | valign="middle" align="center" | 1
| |
| | valign="middle" align="center" | 361
| |
| |-
| |
| | valign="middle" align="center" | 2
| |
| | valign="middle" align="center" | 680
| |
| |-
| |
| | valign="middle" align="center" | 3
| |
| | valign="middle" align="center" | 721
| |
| |-
| |
| | valign="middle" align="center" | 4
| |
| | valign="middle" align="center" | 905
| |
| |-
| |
| | valign="middle" align="center" | 5
| |
| | valign="middle" align="center" | 1010
| |
| |-
| |
| | valign="middle" align="center" | 6
| |
| | valign="middle" align="center" | 1090
| |
| |-
| |
| | valign="middle" align="center" | 7
| |
| | valign="middle" align="center" | 1157
| |
| |-
| |
| | valign="middle" align="center" | 8
| |
| | valign="middle" align="center" | 1330
| |
| |-
| |
| | valign="middle" align="center" | 9
| |
| | valign="middle" align="center" | 1400
| |
| |-
| |
| | valign="middle" align="center" | 10
| |
| | valign="middle" align="center" | 1695
| |
| |}
| |
| | |
| '''Do the following:'''
| |
| | |
| #Plot the data on a Weibull probability plot and obtain the Weibull model parameters.
| |
| #Compute the B10 life of the bulbs.
| |
| | |
| <br>
| |
| | |
| The median ranks for the the <math>{{j}^{th}}</math> failure out of N units is obtained by solving the cumulative binomial equation for <math>Z</math> . This however requires numerical solution. Tables of median ranks can be used in lieu of the solution.
| |
| | |
| | |
| | |
| [http://www.weibull.com/GPaper/ranks2_6.htm Median Rank Tables]
| |
| | |
| <br>
| |
| | |
| <br>
| |
| | |
| represents the rank, or unreliability estimate, for the failure[15; 16] 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>
| |
| | |
| <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>
| |
| | |
| <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>
| |