Life of Incandescent Light Bulbs - Revision history

Lisa Hacker: Replaced content with 'Category: For Deletion'

2015-06-23T21:21:48Z

Replaced content with 'Category: For Deletion'

← Older revision		Revision as of 21:21, 23 June 2015
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>~~

Kate Racaza at 20:55, 27 August 2012

2012-08-27T20:55:19Z

← Older revision		Revision as of 20:55, 27 August 2012
Line 1:		Line 1:
	{{Banner Weibull Examples}}		{{Banner Weibull Examples}}
	<noinclude>[[Category:NTI]]</noinclude>		<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.		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.

Kate Racaza: Undo revision 27937 by Kate Racaza (Talk)

2012-08-27T20:52:47Z

Undo revision 27937 by Kate Racaza (Talk)

← Older revision		Revision as of 20:52, 27 August 2012
Line 1:		Line 1:
	[[Category: ~~For Deletion~~]]		{{Banner Weibull Examples}}
			<noinclude>[[Category:NTI]]</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>

Kate Racaza: does not appear to be linked anywhere

2012-07-27T09:40:17Z

does not appear to be linked anywhere

← Older revision		Revision as of 09:40, 27 July 2012
Line 1:		Line 1:
	~~{{Banner Weibull Examples}}~~		[[Category: For Deletion]]
	~~<noinclude>~~[[Category:~~NTI~~]]~~</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>~~

Kate Racaza at 10:26, 26 July 2012

2012-07-26T10:26:15Z

← Older revision		Revision as of 10:26, 26 July 2012
Line 1:		Line 1:
	{{Banner Weibull Examples}}		{{Banner Weibull Examples}}
			<noinclude>[[Category:NTI]]</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.		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.

Lisa Hacker at 10:46, 20 July 2012

2012-07-20T10:46:05Z

@@ 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.&nbsp; &nbsp;
@@ Line 67: / Line 69: @@
     N  \\
     k  \\
 \end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>

Pantelis at 03:34, 25 June 2011

2011-06-25T03:34:47Z

← Older revision		Revision as of 03:34, 25 June 2011
Line 49:		Line 49:


	[http://www.weibull.com/GPaper/ranks2_6.htm]		[http://www.weibull.com/GPaper/ranks2_6.htm Median Rank Tables]

	<br>		<br>

Pantelis at 03:34, 25 June 2011

2011-06-25T03:34:06Z

← Older revision		Revision as of 03:34, 25 June 2011
Line 45:		Line 45:
	<br>		<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.		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]

			<br>

			<br>

	represents the rank, or unreliability estimate, for the  failure[15; 16] in the following equation for the cumulative binomial:		represents the rank, or unreliability estimate, for the  failure[15; 16] in the following equation for the cumulative binomial:
Line 64:		Line 68:
	k \\		k \\
	\end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>		\end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>






	[[Category:Weibull_Examples]]		[[Category:Weibull_Examples]]

Pantelis at 03:31, 25 June 2011

2011-06-25T03:31:21Z

← Older revision		Revision as of 03:31, 25 June 2011
Line 38:		Line 38:
	\|}		\|}

	'''Do the following:'''		'''Do the following:'''

	#Plot the data on a Weibull probability plot and obtain the Weibull model parameters.		#Plot the data on a Weibull probability plot and obtain the Weibull model parameters.
	#Compute the B10 life of the bulbs.		#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.

	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:



			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}		<math>P=\underset{k=j}{\overset{N}{\mathop \sum }}\,\left( \begin{matrix}
Line 58:		Line 64:
	k \\		k \\
	\end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>		\end{matrix} \right){{Z}^{k}}{{\left( 1-Z \right)}^{N-k}}</math>



	[[Category:Weibull_Examples]]		[[Category:Weibull_Examples]]

Pantelis at 03:27, 25 June 2011

2011-06-25T03:27:34Z

@@ Line 42: / Line 42: @@
 #Plot the data on a Weibull probability plot&nbsp;and obtain the Weibull model parameters.
 #Compute the B10 life of the bulbs.
 [[Category:Weibull_Examples]]