Template:Example: Weibull Distribution Interval Data Example - Revision history

Chris Kahn: Redirected page to Weibull Distribution Examples

2012-08-14T02:15:23Z

Redirected page to Weibull Distribution Examples

← Older revision		Revision as of 02:15, 14 August 2012
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	~~'''Weibull Distribution Interval Data Example'''~~		#REDIRECT [[Weibull Distribution Examples]]

	~~Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:~~

	~~{\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"~~
	~~\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''~~
	~~\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''~~
	~~\| align="center" style="background:~~#~~f0f0f0;"\|'''Time to Failure'''~~
	\|-
	~~\| 1\|\|30\|\|32~~
	\|-
	~~\| 2\|\|32\|\|35~~
	\|-
	~~\| 3\|\|35\|\|37~~
	\|-
	~~\| 4\|\|37\|\|40~~
	\|-
	~~\| 5\|\|42\|\|42~~
	\|-
	~~\| 6\|\|45\|\|45~~
	\|-
	~~\| 7\|\|50\|\|50~~
	\|-
	~~\| 8\|\|55\|\|55~~
	\|-
	\|}

	~~Analyze the data using several different parameter estimation techniques and compare the results.~~

	~~'''Solution'''~~

	~~This data set can be entered into Weibull++ by opening a new '''Data Folio''' and choosing '''Times-to-failure''' and '''My data set contains interval and/or left censored data'''.~~

	[[~~Image: Data Type.png\|center\|550px]]~~

	~~The data is entered as follows,~~

	~~[[Image: Data Folio.png\|center\|550px]]~~

	~~The computed parameters using maximum likelihood are:~~

	~~::<math>\begin{align}~~
	~~& \hat{\beta }=5.76 \\~~
	~~& \hat{\eta }=44.68 \\~~
	~~\end{align}</math>~~

	~~using RRX or rank regression on X:~~

	~~::<math>\begin{align}~~
	~~& \hat{\beta }=5.70 \\~~
	~~& \hat{\eta }=44.54 \\~~
	~~\end{align}</math>~~

	~~and using RRY or rank regression on Y:~~

	~~::<math>\begin{align}~~
	~~& \hat{\beta }=5.41 \\~~
	~~& \hat{\eta }=44.76 \\~~
	~~\end{align}</math>~~

	~~The plot of the MLE solution with the two-sided 90% confidence bounds is:~~
	~~[[Image: MLE Plot.png\|center\|550px~~]]

Richard House at 02:15, 8 August 2012

2012-08-08T02:15:21Z

← Older revision		Revision as of 02:15, 8 August 2012
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	Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:		Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:

	{\| border="1" align="center"		{\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
	\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''		\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''
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	\| 8\|\|55\|\|55		\| 8\|\|55\|\|55
	\|-		\|-
	\|
	\|}		\|}

Richard House at 05:27, 6 August 2012

2012-08-06T05:27:05Z

← Older revision		Revision as of 05:27, 6 August 2012
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	The computed parameters using maximum likelihood are:		The computed parameters using maximum likelihood are:

	~~<center>~~<math>\begin{align}		::<math>\begin{align}
	& \hat{\beta }=5.76 \\		& \hat{\beta }=5.76 \\
	& \hat{\eta }=44.68 \\		& \hat{\eta }=44.68 \\
	\end{align}</math~~></center~~>		\end{align}</math>

	using RRX or rank regression on X:		using RRX or rank regression on X:

	~~<center>~~<math>\begin{align}		::<math>\begin{align}
	& \hat{\beta }=5.70 \\		& \hat{\beta }=5.70 \\
	& \hat{\eta }=44.54 \\		& \hat{\eta }=44.54 \\
	\end{align}</math~~></center~~>		\end{align}</math>

	and using RRY or rank regression on Y:		and using RRY or rank regression on Y:

	~~<center>~~<math>\begin{align}		::<math>\begin{align}
	& \hat{\beta }=5.41 \\		& \hat{\beta }=5.41 \\
	& \hat{\eta }=44.76 \\		& \hat{\eta }=44.76 \\
	\end{align}</math~~></center~~>		\end{align}</math>

	The plot of the MLE solution with the two-sided 90% confidence bounds is:		The plot of the MLE solution with the two-sided 90% confidence bounds is:
	[[Image: MLE Plot.png\|center\|550px]]		[[Image: MLE Plot.png\|center\|550px]]

Richard House at 05:16, 6 August 2012

2012-08-06T05:16:12Z

← Older revision		Revision as of 05:16, 6 August 2012
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	This data set can be entered into Weibull++ by opening a new '''Data Folio''' and choosing '''Times-to-failure''' and '''My data set contains interval and/or left censored data'''.		This data set can be entered into Weibull++ by opening a new '''Data Folio''' and choosing '''Times-to-failure''' and '''My data set contains interval and/or left censored data'''.

	[[Image: Data Type.png~~\|thumb~~\|center\|~~250px~~]]		[[Image: Data Type.png\|center\|550px]]

	The data is entered as follows,		The data is entered as follows,

	[[Image: Data Folio.png~~\|thumb~~\|center\|~~250px~~]]		[[Image: Data Folio.png\|center\|550px]]

	The computed parameters using maximum likelihood are:		The computed parameters using maximum likelihood are:
Line 61:		Line 61:

	The plot of the MLE solution with the two-sided 90% confidence bounds is:		The plot of the MLE solution with the two-sided 90% confidence bounds is:
	[[Image: MLE Plot.png~~\|thumb~~\|center\|~~250px~~]]		[[Image: MLE Plot.png\|center\|550px]]

Nicolette Young at 18:30, 25 April 2012

2012-04-25T18:30:10Z

← Older revision		Revision as of 18:30, 25 April 2012
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	This data set can be entered into Weibull++ by opening a new '''Data Folio''' and choosing '''Times-to-failure''' and '''My data set contains interval and/or left censored data'''.		This data set can be entered into Weibull++ by opening a new '''Data Folio''' and choosing '''Times-to-failure''' and '''My data set contains interval and/or left censored data'''.

	[[Image: Data Type.png\|thumb\|center\|~~400px~~]]		[[Image: Data Type.png\|thumb\|center\|250px]]

	The data is entered as follows,		The data is entered as follows,

	[[Image: Data Folio.png\|thumb\|center\|~~400px~~]]		[[Image: Data Folio.png\|thumb\|center\|250px]]

	The computed parameters using maximum likelihood are:		The computed parameters using maximum likelihood are:

Nicolette Young at 18:29, 25 April 2012

2012-04-25T18:29:45Z

← Older revision		Revision as of 18:29, 25 April 2012
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	Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:		Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:

	{\| border="1"		{\| border="1" align="center"
	\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
	\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''		\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''
Line 61:		Line 61:

	The plot of the MLE solution with the two-sided 90% confidence bounds is:		The plot of the MLE solution with the two-sided 90% confidence bounds is:
	[[Image: MLE Plot.png\|thumb\|center\|~~400px~~]]		[[Image: MLE Plot.png\|thumb\|center\|250px]]

Harry Guo at 22:51, 29 February 2012

2012-02-29T22:51:06Z

← Older revision		Revision as of 22:51, 29 February 2012
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	Analyze the data using several different parameter estimation techniques and compare the results.		Analyze the data using several different parameter estimation techniques and compare the results.

	~~===~~Solution ~~to Weibull Distribution Example 12===~~		'''Solution'''

	This data set can be entered into Weibull++ by opening a new Data Folio and choosing Times-to-failure and My data set contains interval and/or left censored data.		This data set can be entered into Weibull++ by opening a new '''Data Folio''' and choosing '''Times-to-failure''' and '''My data set contains interval and/or left censored data'''.

			[[Image: Data Type.png\|thumb\|center\|400px]]

	The data is entered as follows,		The data is entered as follows,

			[[Image: Data Folio.png\|thumb\|center\|400px]]

	The computed parameters using maximum likelihood are:		The computed parameters using maximum likelihood are:

			<center><math>\begin{align}
			& \hat{\beta }=5.76 \\
			& \hat{\eta }=44.68 \\
			\end{align}</math></center>

	using RRX or rank regression on X:		using RRX or rank regression on X:

			<center><math>\begin{align}
			& \hat{\beta }=5.70 \\
			& \hat{\eta }=44.54 \\
			\end{align}</math></center>

	and using RRY or rank regression on Y:		and using RRY or rank regression on Y:

			<center><math>\begin{align}
			& \hat{\beta }=5.41 \\
			& \hat{\eta }=44.76 \\
			\end{align}</math></center>

	The plot of the MLE solution with the two-sided 90% confidence bounds is:		The plot of the MLE solution with the two-sided 90% confidence bounds is:
			[[Image: MLE Plot.png\|thumb\|center\|400px]]

Harry Guo at 22:46, 29 February 2012

2012-02-29T22:46:26Z

← Older revision		Revision as of 22:46, 29 February 2012
Line 3:		Line 3:
	Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:		Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:

	~~<center>~~{\| border="1"		{\| border="1"
	\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
	\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''		\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''
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	\|-		\|-
	\|		\|
	\|}~~</center>~~		\|}

	Analyze the data using several different parameter estimation techniques and compare the results.		Analyze the data using several different parameter estimation techniques and compare the results.

Harry Guo at 22:46, 29 February 2012

2012-02-29T22:46:04Z

← Older revision		Revision as of 22:46, 29 February 2012
Line 3:		Line 3:
	Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:		Suppose that we have run an experiment with eight units being tested and the following is a table of their last inspection times and times-to-failure:

	~~Table 6.5 - The test data for Example 16~~		<center>{\| border="1"

	~~Data point index~~
	~~Last Inspection~~
	~~Time-to-failure~~
	{\| border="1"
	\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
	\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''		\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''
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	\|-		\|-
	\|		\|
	\|}		\|}</center>

	Analyze the data using several different parameter estimation techniques and compare the results.		Analyze the data using several different parameter estimation techniques and compare the results.

Harry Guo at 22:45, 29 February 2012

2012-02-29T22:45:31Z

← Older revision		Revision as of 22:45, 29 February 2012
Line 8:		Line 8:
	Last Inspection		Last Inspection
	Time-to-failure		Time-to-failure
	1		{\| border="1"
	30		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
	32		\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''
	2		\| align="center" style="background:#f0f0f0;"\|'''Time to Failure'''
	32		\|-
	35		\| 1\|\|30\|\|32
	3		\|-
	35		\| 2\|\|32\|\|35
	37		\|-
	4		\| 3\|\|35\|\|37
	37		\|-
	40		\| 4\|\|37\|\|40
	5		\|-
	42		\| 5\|\|42\|\|42
	42		\|-
	6		\| 6\|\|45\|\|45
	45		\|-
	45		\| 7\|\|50\|\|50
	7		\|-
	50		\| 8\|\|55\|\|55
	50		\|-
	8		\|
	55		\|}
	55
	Analyze the data using several different parameter estimation techniques and compare the results.		Analyze the data using several different parameter estimation techniques and compare the results.