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

Chris Kahn: Redirected page to Weibull Distribution Examples

2012-08-14T02:15:04Z

Redirected page to Weibull Distribution Examples

← Older revision		Revision as of 02:15, 14 August 2012
Line 1:		Line 1:
	~~'''Weibull Distribution Suspension Data Example'''~~		#REDIRECT [[Weibull Distribution Examples]]

	ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. The following Table contains the collected data.

	~~{\| {\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"~~
	~~\|+ '''Widget Test Data'''~~
	~~\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''~~
	~~\| align="center" style="background:#f0f0f0;"\|'''State (F/S)'''~~
	~~\| align="center" style="background:~~#~~f0f0f0;"\|'''Time to Failure'''~~
	\|-
	~~\| 1\|\|F\|\|2~~
	\|-
	~~\| 2\|\|S\|\|3~~
	\|-
	~~\| 3\|\|F\|\|5~~
	\|-
	~~\| 4\|\|S\|\|7~~
	\|-
	~~\| 5\|\|F\|\|11~~
	\|-
	~~\| 6\|\|S\|\|13~~
	\|-
	~~\| 7\|\|S\|\|17~~
	\|-
	~~\| 8\|\|S\|\|19~~
	\|-
	~~\| 9\|\|F\|\|23~~
	\|-
	~~\| 10\|\|F\|\|29~~
	\|-
	~~\| 11\|\|S\|\|31~~
	\|-
	~~\| 12\|\|F\|\|37~~
	\|-
	~~\| 13\|\|S\|\|41~~
	\|-
	~~\| 14\|\|F\|\|43~~
	\|-
	~~\| 15\|\|S\|\|47~~
	\|-
	~~\| 16\|\|S\|\|53~~
	\|-
	~~\| 17\|\|F\|\|59~~
	\|-
	~~\| 18\|\|S\|\|61~~
	\|-
	~~\| 19\|\|S\|\|67~~
	\|-
	\|
	\|}


	~~'''Solution'''~~

	In this example, we see that the number of failures is less than the number of suspensions. This is a very common situation, since reliability tests are often terminated before all units fail due to financial or time constraints. Further, some suspensions will be recorded when a failure occurs that is not due to a legitimate failure mode, such as operator error. In cases such as this, a suspension is recorded, since the unit under test cannot be said to have had a legitimate failure.

	~~This data set can be entered into Weibull++ using Times-to-failure and My data set contains suspensions (right censored data).~~

	[[~~Image: Data Type Example 13.png\|center\|550px]]~~

	~~After enter the data, the data folio looks like:~~

	~~[[Image: Data Folio Example 13.png\|center\|550px~~]]

	~~We will use the two-parameter Weibull to solve this problem. The parameters using maximum likelihood are:~~

	~~::<math>\begin{align}~~
	~~& \hat{\beta }=1.145 \\~~
	~~& \hat{\eta }=65.97 \\~~
	~~\end{align}</math>~~

	~~using RRX:~~

	~~::<math>\begin{align}~~
	~~& \hat{\beta }=0.914\\~~
	~~& \hat{\eta }=79.38 \\~~
	~~\end{align}</math>~~

	~~and using RRY:~~

	~~::<math>\begin{align}~~
	~~& \hat{\beta }=0.895\\~~
	~~& \hat{\eta }=82.02 \\~~
	~~\end{align}</math>~~

Richard House at 02:17, 8 August 2012

2012-08-08T02:17:05Z

← Older revision		Revision as of 02:17, 8 August 2012
Line 76:		Line 76:
	& \hat{\eta }=79.38 \\		& \hat{\eta }=79.38 \\
	\end{align}</math>		\end{align}</math>


	and using RRY:		and using RRY:

Richard House at 02:16, 8 August 2012

2012-08-08T02:16:45Z

← Older revision		Revision as of 02:16, 8 August 2012
Line 3:		Line 3:
	ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. The following Table contains the collected data.		ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. The following Table contains the collected data.

	{\| {\| border="1" ~~class~~="~~wikitable~~" style="~~margin~~: ~~1em auto 1em auto~~"		{\| {\| border="1" align="center" style="border-collapse: collapse;" cellpadding="5" cellspacing="5"
	\|+ '''Widget Test Data'''		\|+ '''Widget Test Data'''
	\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
Line 60:		Line 60:

	After enter the data, the data folio looks like:		After enter the data, the data folio looks like:

	[[Image: Data Folio Example 13.png\|center\|550px]]		[[Image: Data Folio Example 13.png\|center\|550px]]


	We will use the two-parameter Weibull to solve this problem. The parameters using maximum likelihood are:		We will use the two-parameter Weibull to solve this problem. The parameters using maximum likelihood are:

	~~<center>~~<math>\begin{align}		::<math>\begin{align}
	& \hat{\beta }=1.145 \\		& \hat{\beta }=1.145 \\
	& \hat{\eta }=65.97 \\		& \hat{\eta }=65.97 \\
	\end{align}</math~~></center~~>		\end{align}</math>

	using RRX:		using RRX:
	~~<center>~~<math>\begin{align}
			::<math>\begin{align}
	& \hat{\beta }=0.914\\		& \hat{\beta }=0.914\\
	& \hat{\eta }=79.38 \\		& \hat{\eta }=79.38 \\
	\end{align}</math~~></center~~>		\end{align}</math>


	and using RRY:		and using RRY:
	~~<center>~~<math>\begin{align}
			::<math>\begin{align}
	& \hat{\beta }=0.895\\		& \hat{\beta }=0.895\\
	& \hat{\eta }=82.02 \\		& \hat{\eta }=82.02 \\
	\end{align}</math~~></center~~>		\end{align}</math>

Richard House at 05:16, 6 August 2012

2012-08-06T05:16:58Z

← Older revision		Revision as of 05:16, 6 August 2012
Line 57:		Line 57:
	This data set can be entered into Weibull++ using Times-to-failure and My data set contains suspensions (right censored data).		This data set can be entered into Weibull++ using Times-to-failure and My data set contains suspensions (right censored data).

	[[Image: Data Type Example 13.png~~\|thumb~~\|center\|~~250px~~]]		[[Image: Data Type Example 13.png\|center\|550px]]

	After enter the data, the data folio looks like:		After enter the data, the data folio looks like:
	[[Image: Data Folio Example 13.png~~\|thumb~~\|center\|~~250px~~]]		[[Image: Data Folio Example 13.png\|center\|550px]]

Nicolette Young at 18:33, 25 April 2012

2012-04-25T18:33:41Z

← Older revision		Revision as of 18:33, 25 April 2012
Line 57:		Line 57:
	This data set can be entered into Weibull++ using Times-to-failure and My data set contains suspensions (right censored data).		This data set can be entered into Weibull++ using Times-to-failure and My data set contains suspensions (right censored data).

	[[Image: Data Type Example 13.png\|thumb\|center\|~~400px~~]]		[[Image: Data Type Example 13.png\|thumb\|center\|250px]]

	After enter the data, the data folio looks like:		After enter the data, the data folio looks like:
	[[Image: Data Folio Example 13.png\|thumb\|center\|~~400px~~]]		[[Image: Data Folio Example 13.png\|thumb\|center\|250px]]

Harry Guo at 23:17, 29 February 2012

2012-02-29T23:17:30Z

← Older revision		Revision as of 23:17, 29 February 2012
Line 6:		Line 6:
	\|+ '''Widget Test Data'''		\|+ '''Widget Test Data'''
	\| 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;"\|'''State (F/S)'''
	\| align="center" style="background:#f0f0f0;"\|'''Time to Failure'''		\| align="center" style="background:#f0f0f0;"\|'''Time to Failure'''
	\|-		\|-

Harry Guo at 23:01, 29 February 2012

2012-02-29T23:01:04Z

← Older revision		Revision as of 23:01, 29 February 2012
Line 1:		Line 1:
	'''Weibull Distribution Suspension Data Example'''		'''Weibull Distribution Suspension Data Example'''

	ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. Table ~~6.6~~ contains the collected data.		ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. The following Table contains the collected data.

	{\| {\| border="1" class="wikitable" style="margin: 1em auto 1em auto"		{\| {\| border="1" class="wikitable" style="margin: 1em auto 1em auto"

Harry Guo at 23:00, 29 February 2012

2012-02-29T23:00:44Z

← Older revision		Revision as of 23:00, 29 February 2012
Line 4:		Line 4:

	{\| {\| border="1" class="wikitable" style="margin: 1em auto 1em auto"		{\| {\| border="1" class="wikitable" style="margin: 1em auto 1em auto"
	\|+ Widget Test Data		\|+ '''Widget Test Data'''
	\| 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'''

Harry Guo at 23:00, 29 February 2012

2012-02-29T23:00:30Z

← Older revision		Revision as of 23:00, 29 February 2012
Line 1:		Line 1:
	==Weibull Distribution Example ~~13==~~		'''Weibull Distribution Suspension Data Example'''

	ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. Table 6.6 contains the collected data.		ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. Table 6.6 contains the collected data.
Line 49:		Line 49:
	\|		\|
	\|}		\|}
	~~===~~Solution ~~to Weibull Distribution Example 13===~~

			'''Solution'''

	In this example, we see that the number of failures is less than the number of suspensions. This is a very common situation, since reliability tests are often terminated before all units fail due to financial or time constraints. Further, some suspensions will be recorded when a failure occurs that is not due to a legitimate failure mode, such as operator error. In cases such as this, a suspension is recorded, since the unit under test cannot be said to have had a legitimate failure.		In this example, we see that the number of failures is less than the number of suspensions. This is a very common situation, since reliability tests are often terminated before all units fail due to financial or time constraints. Further, some suspensions will be recorded when a failure occurs that is not due to a legitimate failure mode, such as operator error. In cases such as this, a suspension is recorded, since the unit under test cannot be said to have had a legitimate failure.

	This data set can be entered into Weibull++ using Times-to-failure and My data set contains suspensions (right censored data).		This data set can be entered into Weibull++ using Times-to-failure and My data set contains suspensions (right censored data).

			[[Image: Data Type Example 13.png\|thumb\|center\|400px]]

			After enter the data, the data folio looks like:
			[[Image: Data Folio Example 13.png\|thumb\|center\|400px]]


	We will use the two-parameter Weibull to solve this problem. The parameters using maximum likelihood are:		We will use the two-parameter Weibull to solve this problem. The parameters using maximum likelihood are:

			<center><math>\begin{align}
			& \hat{\beta }=1.145 \\
			& \hat{\eta }=65.97 \\
			\end{align}</math></center>

	using RRX:		using RRX:
			<center><math>\begin{align}
			& \hat{\beta }=0.914\\
			& \hat{\eta }=79.38 \\
			\end{align}</math></center>


	and using RRY:		and using RRY:
			<center><math>\begin{align}
			& \hat{\beta }=0.895\\
			& \hat{\eta }=82.02 \\
			\end{align}</math></center>

Harry Guo at 22:55, 29 February 2012

2012-02-29T22:55:09Z

← Older revision		Revision as of 22:55, 29 February 2012
Line 3:		Line 3:
	ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. Table 6.6 contains the collected data.		ACME company manufactures widgets, and is currently engaged in reliability testing a new widget design. Nineteen units are being reliability tested, but due to the tremendous demand for widgets, units are removed from the test whenever the production cannot cover the demand. The test is terminated at the 67th day when the last widget is removed from the test. Table 6.6 contains the collected data.

	~~Table 6.6 -~~ Widget ~~test data~~		{\| {\| border="1" class="wikitable" style="margin: 1em auto 1em auto"
			\|+ Widget Test Data
	Data ~~point index~~		\| align="center" style="background:#f0f0f0;"\|'''Data Point Index'''
	~~State (S or F)~~		\| align="center" style="background:#f0f0f0;"\|'''Last Inspection'''
	Time-to-~~failure~~		\| align="center" style="background:#f0f0f0;"\|'''Time to Failure'''
	1		\|-
	F		\| 1\|\|F\|\|2
	2		\|-
	2		\| 2\|\|S\|\|3
	S		\|-
	3		\| 3\|\|F\|\|5
	3		\|-
	F		\| 4\|\|S\|\|7
	5		\|-
	4		\| 5\|\|F\|\|11
	S		\|-
	7		\| 6\|\|S\|\|13
	5		\|-
	F		\| 7\|\|S\|\|17
	11		\|-
	6		\| 8\|\|S\|\|19
	S		\|-
	13		\| 9\|\|F\|\|23
	7		\|-
	S		\| 10\|\|F\|\|29
	17		\|-
	8		\| 11\|\|S\|\|31
	S		\|-
	19		\| 12\|\|F\|\|37
	9		\|-
	F		\| 13\|\|S\|\|41
	23		\|-
	10		\| 14\|\|F\|\|43
	F		\|-
	29		\| 15\|\|S\|\|47
	11		\|-
	S		\| 16\|\|S\|\|53
	31		\|-
	12		\| 17\|\|F\|\|59
	F		\|-
	37		\| 18\|\|S\|\|61
	13		\|-
	S		\| 19\|\|S\|\|67
	41		\|-
	14		\|
	F		\|}
	43
	15
	S
	47
	16
	S
	53
	17
	F
	59
	18
	S
	61
	19
	S
	67
	===Solution to Weibull Distribution Example 13===		===Solution to Weibull Distribution Example 13===