Life of Incandescent Light Bulbs: Difference between revisions

From ReliaWiki
Jump to navigation Jump to search
No edit summary
(Replaced content with 'Category: For Deletion')
 
(8 intermediate revisions by 3 users not shown)
Line 1: Line 1:
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.
 
 
 
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:
 
<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

Retrieved from "https://www.reliawiki.com/index.php?title=Life_of_Incandescent_Light_Bulbs&oldid=58418"