Life of Incandescent Light Bulbs: Difference between revisions

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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]]
 
{| 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&nbsp; for&nbsp;the &nbsp;the <math>{{j}^{th}}</math>&nbsp;failure out of N&nbsp;units is obtained by solving the cumulative binomial equation for <math>Z</math> . This however requires numerical solution.&nbsp; Tables of median ranks can be used in lieu of the solution.
 
 
 
[http://www.weibull.com/GPaper/ranks2_6.htm]
 
<br>
 
<br>
 
represents the rank, or unreliability estimate, for the&nbsp; 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>
 
 
 
 
 
[[Category:Weibull_Examples]]

Latest revision as of 21:21, 23 June 2015

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